Fixed Point Theory In Ordered Sets And Applications

Author : Siegfried Carl,Seppo Heikkilä
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 53,6 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441975850

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Fixed Point Theory in Ordered Sets and Applications by Siegfried Carl,Seppo Heikkilä Pdf

This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

Author : Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 48,6 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9783319015866

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Topics in Fixed Point Theory by Saleh Almezel,Qamrul Hasan Ansari,Mohamed Amine Khamsi Pdf

The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. 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 function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.

Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 45,5 Mb
Release : 2001-03-22
Category : Mathematics
ISBN : 9781139433792

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Fixed Point Theory and Applications by Ravi P. Agarwal,Maria Meehan,Donal O'Regan Pdf

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Author : Praveen Agarwal,Mohamed Jleli,Bessem Samet
Publisher : Springer
Page : 166 pages
File Size : 53,8 Mb
Release : 2018-10-13
Category : Mathematics
ISBN : 9789811329135

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Fixed Point Theory in Metric Spaces by Praveen Agarwal,Mohamed Jleli,Bessem Samet Pdf

This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials. The book is a valuable resource for a wide audience, including graduate students and researchers.

Author : Monther Alfuraidan,Qamrul Ansari
Publisher : Academic Press
Page : 442 pages
File Size : 46,8 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9780128043653

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Fixed Point Theory and Graph Theory by Monther Alfuraidan,Qamrul Ansari Pdf

Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications

Author : Yeol Je Cho
Publisher : Nova Publishers
Page : 220 pages
File Size : 53,7 Mb
Release : 2002
Category : Mathematics
ISBN : 1590331893

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Fixed Point Theory and Applications by Yeol Je Cho Pdf

Fixed Point Theory & Applications Volume II

Author : Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro
Publisher : Springer Nature
Page : 503 pages
File Size : 54,5 Mb
Release : 2021-06-05
Category : Mathematics
ISBN : 9789813366473

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Advances in Metric Fixed Point Theory and Applications by Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro Pdf

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.

Author : Clement Ampadu
Publisher : Lulu.com
Page : 46 pages
File Size : 44,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9781365563607

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Higher-Order Fixed Point Theory in Partial Metric Spaces: Some Results Generalizing the Hardy-Rogers Map by Clement Ampadu Pdf

Author : Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro
Publisher : Springer
Page : 385 pages
File Size : 53,7 Mb
Release : 2016-03-24
Category : Mathematics
ISBN : 9783319240824

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Fixed Point Theory in Metric Type Spaces by Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro Pdf

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.

Author : Yeol Je Cho,Jong Kyu Kim
Publisher : Nova Publishers
Page : 222 pages
File Size : 44,5 Mb
Release : 2007
Category : Mathematics
ISBN : 1594548730

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Fixed Point Theory and Applications, Volume 6 by Yeol Je Cho,Jong Kyu Kim Pdf

Fixed Point Theory & Applications

Author : Józef Banaś,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro
Publisher : Springer
Page : 487 pages
File Size : 46,7 Mb
Release : 2017-04-25
Category : Mathematics
ISBN : 9789811037221

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Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness by Józef Banaś,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro Pdf

This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.

Author : P. V. Subrahmanyam
Publisher : Unknown
Page : 302 pages
File Size : 52,5 Mb
Release : 2018
Category : Global analysis (Mathematics)
ISBN : 9811331596

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Elementary Fixed Point Theorems by P. V. Subrahmanyam Pdf

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky's theorem on periodic points, Thron's results on the convergence of certain real iterates, Shield's common fixed theorem for a commuting family of analytic functions and Bergweiler's existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski's theorem by Merrifield and Stein and Abian's proof of the equivalence of Bourbaki-Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward's theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka's proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy-Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder-Gohde-Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.

Author : Andrzej Granas,James Dugundji
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 48,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9780387215938

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Fixed Point Theory by Andrzej Granas,James Dugundji Pdf

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS

Author : Bernd Schröder
Publisher : Birkhäuser
Page : 420 pages
File Size : 46,8 Mb
Release : 2016-05-11
Category : Mathematics
ISBN : 9783319297880

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Ordered Sets by Bernd Schröder Pdf

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Author : Hsien-ChungWu
Publisher : MDPI
Page : 236 pages
File Size : 41,8 Mb
Release : 2020-03-13
Category : Mathematics
ISBN : 9783039284320

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Fixed Point Theory and Related Topics by Hsien-ChungWu Pdf

Fixed point theory arose from the Banach contraction principle and has been studied for a long time. Its application mostly relies on the existence of solutions to mathematical problems that are formulated from economics and engineering. After the existence of the solutions is guaranteed, the numerical methodology will be established to obtain the approximated solution. Fixed points of function depend heavily on the considered spaces that are defined using the intuitive axioms. In particular, variant metrics spaces are proposed, like a partial metric space, b-metric space, fuzzy metric space and probabilistic metric space, etc. Different spaces will result in different types of fixed point theorems. In other words, there are a lot of different types of fixed point theorems in the literature. Therefore, this Special Issue welcomes survey articles. Articles that unify the different types of fixed point theorems are also very welcome. The topics of this Special Issue include the following: Fixed point theorems in metric space Fixed point theorems in fuzzy metric space Fixed point theorems in probabilistic metric space Fixed point theorems of set-valued functions in various spaces The existence of solutions in game theory The existence of solutions for equilibrium problems The existence of solutions of differential equations The existence of solutions of integral equations Numerical methods for obtaining the approximated fixed points