File | Description | Size | Format | |
---|---|---|---|---|
Attached File | 54.01 kB | Adobe PDF | ||
2.32 MB | Adobe PDF | |||
553.75 kB | Adobe PDF | |||
89.18 kB | Adobe PDF | |||
236.86 kB | Adobe PDF | |||
179.07 kB | Adobe PDF | |||
205.21 kB | Adobe PDF | |||
194.46 kB | Adobe PDF | |||
190.21 kB | Adobe PDF | |||
228.36 kB | Adobe PDF | |||
223.96 kB | Adobe PDF | |||
193.62 kB | Adobe PDF | |||
94.05 kB | Adobe PDF | |||
305.39 kB | Adobe PDF | |||
1.18 MB | Adobe PDF |
Items in Shodhganga are licensed under Creative Commons Licence Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0).
Breadcrumbs Section. Click here to navigate to respective pages.
Metric Structures and Fixed Point Theory
DOI link for Metric Structures and Fixed Point Theory
It is an indisputable argument that the formulation of metrics (by Fréchet in the early 1900s) opened a new subject in mathematics called non-linear analysis after the appearance of Banach’s fixed point theorem. Because the underlying space of this theorem is a metric space, the theory that developed following its publication is known as metric fixed point theory. It is well known that metric fixed point theory provides essential tools for solving problems arising in various branches of mathematics and other sciences such as split feasibility problems, variational inequality problems, non-linear optimization problems, equilibrium problems, selection and matching problems, and problems of proving the existence of solutions of integral and differential equations are closely related to fixed point theory. For this reason, many people over the past seventy years have tried to generalize the definition of metric space and corresponding fixed point theory. This trend still continues. A few questions lying at the heart of the theory remain open and there are many unanswered questions regarding the limits to which the theory may be extended.
Metric Structures and Fixed Point Theory provides an extensive understanding and the latest updates on the subject. The book not only shows diversified aspects of popular generalizations of metric spaces such as symmetric, b -metric, w -distance, G -metric, modular metric, probabilistic metric, fuzzy metric, graphical metric and corresponding fixed point theory but also motivates work on existing open problems on the subject. Each of the nine chapters—contributed by various authors—contains an Introduction section which summarizes the material needed to read the chapter independently of the others and contains the necessary background, several examples, and comprehensive literature to comprehend the concepts presented therein. This is helpful for those who want to pursue their research career in metric fixed point theory and its related areas.
This book serves as a reference for scientific investigators who need to analyze a simple and direct presentation of the fundamentals of the theory of metric fixed points. It may also be used as a text book for postgraduate and research students who are trying to derive future research scope in this area.
Chapter 1 | 30 pages, symmetric spaces and fixed point theory, chapter chapter 2 | 34 pages, fixed point theory in b-metric spaces, chapter chapter 3 | 36 pages, basics of w-distance and its use in various types of results, chapter chapter 4 | 46 pages, g-metric spaces: from the perspective of f-contractions and best proximity points, chapter chapter 5 | 50 pages, fixed point theory in probabilistic metric spaces, chapter chapter 6 | 46 pages, fixed point theory for fuzzy contractive mappings, chapter chapter 7 | 22 pages, set-valued maps and inclusion problems inmodular metric spaces, chapter chapter 8 | 16 pages, graphical metric spaces and fixed point theorems, chapter chapter 9 | 16 pages, fixed point theory in partial metric spaces.
Connect with us
Registered in England & Wales No. 3099067 5 Howick Place | London | SW1P 1WG © 2024 Informa UK Limited
This thematic series is devoted to publishing the latest and most significant research on Fixed Point Theory including its wide range of applications. Its goals are to stimulate further research and to highlight and emphasize the most recent advances in the field as well as to promote, encourage, and bring together researchers in Fixed point Theory and Applications including those interested in potential applications in Science and Engineering.
Edited by: Yeol Je Cho, Manuel De la Sen, Abdul Latif and Reza Saadati
This paper provides new common fixed point theorems for pairs of multivalued and single-valued mappings operating between ordered Banach spaces. Our results lead to new existence theorems for a system of integ...
We define a new version of proximal C -contraction and prove the existence and uniqueness of a common best proximity point for a pair of non-self functions. Then we apply our main results to get some fixed point t...
In this paper we consider a class of bilevel variational inequalities with hierarchical nesting structure. We first of all get the existence of a solution for this problem by using the Himmelberg fixed point t...
Motivated by Gopal et al. (Acta Math. Sci. 36B(3):1-14, 2016 ). We introduce the notion of α -type F -contraction in the setting of modular metric spaces which is independent from one given in (Hussain et al. in Fix...
Variational inequality formulation of circular cone eigenvalue complementarity problems.
In this paper, we study the circular cone eigenvalue complementarity problem (CCEiCP) by variational inequality technique, prove the existence of a solution to CCEiCP, and investigate different nonlinear progr...
In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the firs...
A coupled fixed point theorem and application to fractional hybrid differential problems, common fixed point results of a pair of generalized \((\psi,\varphi )\) -contraction mappings in modular spaces.
In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some fixed and common fixed point results for such mappings...
On best proximity points of upper semicontinuous multivalued mappings, unification of several distance functions and a common fixed point result, iterative algorithms for infinite accretive mappings and applications to p -laplacian-like differential systems.
Some new iterative algorithms with errors for approximating common zero point of an infinite family of m -accretive mappings in a real Banach space are presented. A path convergence theorem and some new weak and s...
In this paper, we propose an iterative algorithm and, by using the proposed algorithm, prove some strong convergence theorems for finding a common element of the set of solutions of a finite family of split eq...
In this paper, we introduce the two new concepts of an α -type almost- F -contraction and an α -type F Suzuki contraction and prove some fixed point theorems for such mappings in a complete metric space. Some example...
We compare the rate of convergence for some iteration methods for contractions. We conclude that the coefficients involved in these methods have an important role to play in determining the speed of the conver...
The aim of this paper to present fixed point results for single-valued operators in b -metric spaces. The case of scalar metric and the case of vector-valued metric approaches are considered. As an application, a ...
By processing the problem through fixed point theory and propagator theory, we investigate the periodicity of solutions to a class of impulsive evolution equations in Hilbert spaces and establish some existenc...
In this paper, we provide a new approach for discussing the solvability of a class of operator equations by establishing fixed point theorems in locally convex spaces. Our results are obtained extend some Kras...
A fixed point result and the stability problem in lie superalgebras.
In this paper, we introduce the concept of normed Lie superalgebras and define the superhomomorphism and the superderivation in normed Lie superalgebras. We define a generalized T -orbitally complete metric space ...
In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems ...
In this paper, we investigate the sufficient condition for the existence of best proximity points for non-self-multivalued mappings. Additionally, we discuss the stability theorem for such mappings. Our result...
An intermixed algorithm for two strict pseudo-contractions in Hilbert spaces have been presented. It is shown that the suggested algorithms converge strongly to the fixed points of two strict pseudo-contractio...
The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we ...
In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a conti...
Very recently, Fang (Fuzzy Sets Syst. 267:86-99, 2015) gave some fixed point theorems for probabilistic φ -contractions in Menger spaces. Fang’s results improve the one of Jachymski (Nonlinear Anal. 73:2199-2203, ...
On fixed point theory in topological posets, extended quasi-metric spaces and an application to asymptotic complexity of algorithms.
In this paper we present a few fixed point results in the framework of topological posets. To this end, we introduce an appropriate notion of completeness and order-continuity. Special attention is paid to the...
The main aim of this paper is to obtain some new common fixed point theorems for Geraghty’s type contraction mappings using the monotone property with two metrics and to give some examples to illustrate the ma...
The purpose of this paper is to study stability and strong convergence of asymptotically pseudocontractive mappings by using a new composite implicit iteration process in an arbitrary real Banach space. The re...
In this paper, a new type of G -contraction multivalued mappings in a metric space endowed with a directed graph is introduced and studied. This type of mappings is more general than that of Mizoguchi and Takahash...
In this paper we establish some best proximity point results using generalized weak contractions with discontinuous control functions. The theorems are established in metric spaces with a partial order. We vie...
It is well known that equilibrium problems are very important mathematical models and are closely related with fixed point problems, variational inequalities, and Nash equilibrium problems. Gap functions and e...
Common fixed point results for four maps satisfying ϕ -contractive condition in multiplicative metric spaces.
In this paper, we consider the setting of multiplicative metric spaces to establish results regarding the common fixed points of four mappings, using a contraction condition defined by means of a comparison fu...
In this paper, we introduce the notion of generalized cyclic contraction pairs in b -metric spaces and establish some fixed point theorems for such pairs. Also, we give some examples to illustrate the main results...
Fixed point results for generalized f -contractions in modular metric and fuzzy metric spaces.
The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F -contraction in modular metric spac...
Endpoints of multivalued nonexpansive mappings in geodesic spaces.
Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if...
In this paper, two iteration processes are used to find the solutions of the mathematical programming for the sum of two convex functions. In infinite Hilbert space, we establish two strong convergence theorem...
New multipled common fixed point theorems in menger pm-spaces.
arXiv's Accessibility Forum starts next month!
Help | Advanced Search
Title: common fixed point theorems for a commutative family of nonexpansive mappings in complete random normed modules.
Abstract: In this paper, we first introduce and study the notion of random Chebyshev centers. Further, based on the recently developed theory of stable sets, we introduce the notion of random complete normal structure so that we can prove the two deeper theorems: one of which states that random complete normal structure is equivalent to random normal structure for an $L^0$-convexly compact set in a complete random normed module; the other of which states that if $G$ is an $L^0$-convexly compact subset with random normal structure of a complete random normed module, then every commutative family of nonexpansive mappings from $G$ to $G$ has a common fixed point. We also consider the fixed point problems for isometric mappings in complete random normed modules. Finally, as applications of the fixed point theorems established in random normed modules, when the measurable selection theorems fail to work, we can still prove that a family of strong random nonexpansive operators from $(\Omega,\mathcal{F},P)\times C$ to $C$ has a common random fixed point, where $(\Omega,\mathcal{F},P)$ is a probability space and $C$ is a weakly compact convex subset with normal structure of a Banach space.
Subjects: | Functional Analysis (math.FA) |
Cite as: | [math.FA] |
(or [math.FA] for this version) | |
Focus to learn more arXiv-issued DOI via DataCite |
Access paper:.
Code, data and media associated with this article, recommenders and search tools.
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .
You can also search for this editor in PubMed Google Scholar
Department of mathematics, aligarh muslim university, aligarh, india, department of mathematics and computer sciences, university of palermo, palermo, italy.
8204 Accesses
21 Citations
1 Altmetric
This is a preview of subscription content, log in via an institution to check access.
Subscribe and save.
Tax calculation will be finalised at checkout
Licence this eBook for your library
Institutional subscriptions
This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators.
This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.
Front matter, the relevance of a metric condition on a pair of operators in common fixed point theory.
Yeol Je Cho
Mohamed Jleli, Bessem Samet
Mohammad Mursaleen
Calogero Vetro
YEOL JE CHO is Emeritus Professor at the Department of Mathematics Education, Gyeongsang National University, Jinju, Korea, and Distinguished Professor at the School of Mathematical Sciences, the University of Electronic Science and Technology of China, Chengdu, Sichuan, China. In 1984, he received his Ph.D. in Mathematics from Pusan National University, Pusan, Korea. He is a fellow of the Korean Academy of Science and Technology, Seoul, Korea, since 2006, and a member of several mathematical societies. He has organized international conferences on nonlinear functional analysis and applications, fixed point theory and applications and workshops and symposiums on nonlinear analysis and applications. He has published over 400 papers, 20 monographs and 12 books with renowned publishers from around the world. His research areas are nonlinear analysis and applications, especially fixed point theory and applications, some kinds of nonlinear problems, that is, equilibrium problems, variational inequality problems, saddle point problems, optimization problems, inequality theory and applications, stability of functional equations and applications. He has delivered several invited talks at international conferences on nonlinear analysis and applications and is on the editorial boards of 10 international journals of mathematics.
MOHAMED JLELI is Full Professor of Mathematics at King Saud University, Saudi Arabia. He received his Ph.D. in Pure Mathematics with the thesis entitled “Constant Mean Curvature Hypersurfaces” from the Faculty of Sciences of Paris VI, France, in 2004. His research interests include surfaces and hypersurfaces in space forms, mean curvature, nonlinear partial differential equations, nonlinear fractional calculus and nonlinear analysis, on which he has published his research articles in international journals of repute. He is on the editorial board member of several international journals of mathematics.
MOHAMMAD MURSALEEN is Professor at the Department of Mathematics, Aligarh Muslim University (AMU), India. He is currently Principal Investigator for a SERB Core Research Grant at the Department of Mathematics, AMU, India. He is also Visiting Professor at China Medical University, Taiwan, since January 2019. He has served as Lecturer to Full Professor at AMU since 1982 and as Chair of the Department of Mathematics from 2015 to 2018. He has published more than 350 research papers in the field of summability, sequence spaces, approximation theory, fixed point theory and measures of noncompactness and has authored/co-edited 9 books. Besides several master’s students, he has guided 21 Ph.D. students. He served as a reviewer for various international scientific journals and is on the editorial boards of many international scientific journals. He is on the list of Highly Cited Researchers for the year 2019 of Thomson Reuters (Web of Science).
BESSEM SAMET is Full Professor of Applied Mathematics at King Saud University, Saudi Arabia. He received his Ph.D. in Applied Mathematics with the thesis entitled “Topological Derivative Method for Maxwell Equations and its Applications” from Paul Sabatier University, France, in 2004. His areas of research include different branches of nonlinear analysis, including fixed point theory, partial differential equations, fractional calculus and more. He has authored/co-authored over 100 published research papers in ISI journals. He was on the list of Thomson Reuters Highly Cited Researchers for the years 2015 to 2017.
CALOGERO VETRO is Assistant Professor of Mathematical Analysis at the University of Palermo, Italy, since 2005. He is also affiliated with the Department of Mathematics and Computer Science of the university. He received his Ph.D. in Engineering of Automation and Control Systems in 2004 and the Laurea Degree in Mechanical Engineering in 2000. He has taught courses in mathematical analysis, numerical analysis, numerical calculus, geomathematics, computational mathematics, operational research and optimization. He is a member of Doctoral Collegium at the University of Palermo and acts as a referee for several scientific journals of pure and applied mathematics. He is also on the editorial boards of renowned scientific journals and a guest editor of special issues on fixed point theory and partial differential equations. His research interests include approximation, fixed point theory, functional analysis, mathematical programming, operator theory and partial differential equations. He has authored/co-authored over 150 published papers and was on the Thomson Reuters Highly Cited Researchers List from 2015 to 2017.
Book Title : Advances in Metric Fixed Point Theory and Applications
Editors : Yeol Je Cho, Mohamed Jleli, Mohammad Mursaleen, Bessem Samet, Calogero Vetro
DOI : https://doi.org/10.1007/978-981-33-6647-3
Publisher : Springer Singapore
eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)
Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
Hardcover ISBN : 978-981-33-6646-6 Published: 04 May 2021
Softcover ISBN : 978-981-33-6649-7 Published: 05 May 2022
eBook ISBN : 978-981-33-6647-3 Published: 04 May 2021
Edition Number : 1
Number of Pages : XVII, 503
Number of Illustrations : 5 b/w illustrations, 1 illustrations in colour
Topics : Functional Analysis , Topology , Operator Theory
Policies and ethics
Thumbnail | Title | Date Uploaded | Visibility | Actions |
---|---|---|---|---|
2021-01-04 | Public |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
History of the brouwer fixed point theorem, introduction to: topological degree and fixed point theories in differential and difference equations, variational principles and critical point theory, partial differential equations in the 20 th century *, a topological degree of type (s) for hammerstein operators, variational inequalities,bifurcation and applications, the bolzano mean-value theorem and partial differential equations, on the periodic solutions of discontinuous piecewise differential systems, the degree theory for set-valued compact perturbation of monotone-type mappings with an application.
31 references, on the uniqueness of the topological degree, the topological degree for noncompact nonlinear mappings in banach spaces, topology and nonlinear boundary value problems, nonlinear functional analysis, degree of mapping for nonlinear mappings of monotone type., the leray-schauder index and the fixed point theory for arbitrary anrs, some historical remarks concerning degree theory, topologie et équations fonctionnelles.
Degree theory for local condensing maps, related papers.
Showing 1 through 3 of 0 Related Papers
Discover the world's research
PDF Version Also Available for Download.
Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development … continued below
Farmer, Matthew Ray December 2005.
This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by the UNT Libraries to the UNT Digital Library , a digital repository hosted by the UNT Libraries . It has been viewed 2293 times, with 4 in the last month. More information about this thesis can be viewed below.
People and organizations associated with either the creation of this thesis or its content.
For guidance see Citations, Rights, Re-Use .
Unt libraries.
The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.
Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.
Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces replaced by uniformly convex Banach spaces.
Unique identifying numbers for this thesis in the Digital Library or other systems.
This thesis is part of the following collection of related materials.
Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community .
What responsibilities do I have when using this thesis?
Dates and time periods associated with this thesis.
When was this thesis last used?
Here are some suggestions for what to do next.
We support the IIIF Presentation API
Links for robots.
Helpful links in machine-readable formats.
Farmer, Matthew Ray. Applications in Fixed Point Theory , thesis , December 2005; Denton, Texas . ( https://digital.library.unt.edu/ark:/67531/metadc4971/ : accessed August 24, 2024 ), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu ; .
COMMENTS
Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2019. ... Fixed point theory be one of the advanced topics in both pure and applied mathematics, it also has seen great interest since recent decades, because it is considered an essential tool for nonlinear analysis and many other branches of ...
Some of these applications involve obtaining new. metrics on a space, forcing a continuous map to have a fixed point, and using. conditions on the boundary of a closed ball in a Banach space to obtain a fixed point. Finally, a development of the theorem due to Browder et al. is given with Hilbert spaces.
Fixed point theory is a very natural and well developed but still a young domain. ... Throughout this thesis, the set of fixed points of a mapping. f. is denoted by. Fi x (f),
FIXED POINT THEOREMS THESIS SUBMITTED FOR THE AWARD OF THE DEGREE OF Doctor of Philosophy IN APPLIED MATHEMATICS BY RAHUL BHARADWAJ ... fixed points. Fixed point theory is an important area in the fast growing fields of non-linear analysis and non-linear operators. It is relatively young and fully
This thesis is a work on fixed point theorems in complex valued metric spaces. This thesis comprises of eight chapters. Every chap- ter has two or three sections. ... . newline newline The first chapter of thesis is named as introduction which includes definition and significance of fixed point theory, historical background, definition and ...
The metric fixed point theorem is based on the Banach contracti on principle, which was introduced in 1922. and has affected m any aspects of nonlinear functional analysis. The m ethod is based on ...
This paper is an exposition of the Brouwer Fixed-Point Theorem of topology and the Three Points Theorem of transformational plane geometry. If we consider a set X and a function f : X!X, a xed point of f is a point x2Xsuch that f(x) = x. Brouwer's Fixed-Point Theorem states that every continuous function from the n-ball Bn to itself has
The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular ...
Ph.D. Thesis FIXED POINTS THEOREMS IN METRIC SPACES ENDOWED WITH A GRAPH Scientificadvisor: Ph.D.Student: Prof. Univ. Dr. Vasile Berinde Bojor Florin BaiaMare 2012. Contents ... The Fixed Point Theory is one of the most powerful and productive tools from
Description of various generalizations of metric spaces. Very new topics on fixed point theory in graphical and modular metric spaces. Enriched with examples and open problems. This book serves as a reference for scientific investigators who need to analyze a simple and direct presentation of the fundamentals of the theory of metric fixed points.
This paper provides new common fixed point theorems for pairs of multivalued and single-valued mappings operating between ordered Banach spaces. Our results lead to new existence theorems for a system of integ... Nawab Hussain and Mohamed-Aziz Taoudi. Fixed Point Theory and Applications 2016 2016 :65. Research Published on: 31 May 2016.
One such result is Schauder's fixed point theorem. This theorem is broadly applicable in proving the existence of solutions to differential equations, including the Navier-Stokes equations under certain conditions. Recently a semi-constructive proof of Schauder's theorem was developed in Rizzolo and Su (2007).
The study on Banach Fixed Point Theorem and its Applications is a motivation of the development of Banach fixed point theorem. Polish Mathematician Stefan Banach had discussed Banach fixed point theorem as a part of his PhD thesis in 1922. Here, Banach contrac-tion principle and Banach fixed point theorem is important for nonlinear analy-sis.
In this PhD Thesis, we present our contribution to Fixed Point Theory and some appli-cations to Iteration Processes and Variational Inequalities. The study is motivated by nowadays research developed by leading scientists and by its possible development for real world applications; please, see: Bakhtin [7], Banach [8], Berinde [13], Czerwick [19],
View PDF HTML (experimental) Abstract: In this paper, we first introduce and study the notion of random Chebyshev centers. Further, based on the recently developed theory of stable sets, we introduce the notion of random complete normal structure so that we can prove the two deeper theorems: one of which states that random complete normal structure is equivalent to random normal structure for ...
Abstract. "The theory of fixed points is one of the most powerful tools of modern mathematics" quoted by Felix Browder, gave a new impetus to the modern fixed point theory via the development of nonlinear functional analysis as an active and vital branch of mathematics. The flourishing field of fixed point theory started in the early days ...
3 Department of l,larhemarical Sciences, Kathnnndu lJniversity, P.O. Box 6250, K at hmondu, N e pa l. E- mai I : j ha knh@1'ah o o. c o. i n. In this paper, we present a brief historical account ...
This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically ...
Masters Thesis Fixed point theory : Banach, Brouwer and Schauder theorems. The primary focus of this work is the Brouwer and Schauder fixed point (points that are mapped onto itself) theorems. These theorems give the existence for the presence of fixed points in normed linear spaces. Brouwer considers finite-dimensional spaces while Schauder ...
4.6 Approximate fixed points 89 4.7 Isbell's hyperconvex hull 91 Exercises 98 5 "Normal" Structures in Metric Spaces 101 5.1 A fixed point theorem 101 5.2 Structure of the fixed point set 103 5.3 Uniform normal structure 106 5.4 Uniform relative normal structure 110 5.5 Quasi-normal structure 112 5.6 Stability and normal structure 115
Fixed point theory and nonlinear problems. Introduction. Among the most original and far-reaching of the contributions made by Henri Poincare to mathematics was his introduction of the use of topological or "qualitative" methods in the study of nonlinear problems in analysis. His starting point was the study of the differential equations of ...
1 [email protected], 2 [email protected]. Abstract - Fixed point theory is developed to find out the fixed point for selfmaps in Metric Space. The famous Mathematician H. Poincare ...
Banach's contraction principle is probably one of the most important theorems in fixed point theory. It has been used to develop much of the rest of fixed point theory. Another key result in the field is a theorem due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications ...
The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. [2]By contrast, the Brouwer fixed-point theorem (1911) is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, [3] but it doesn ...