Generalized Metric Spaces And Mappings

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Generalized Metric Spaces and Mappings

Shou Lin,Ziqiu Yun
Generalized Metric Spaces and Mappings Book PDF

Author : Shou Lin,Ziqiu Yun
Publisher : Springer
Page : 328 pages
File Size : 44,9 Mb
Release : 2016-10-20
Category : Mathematics
ISBN : 9789462392168

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Generalized Metric Spaces and Mappings by Shou Lin,Ziqiu Yun Pdf

The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.

Fixed Point Theory in Generalized Metric Spaces

Erdal Karapinar,Ravi P. Agarwal
Fixed Point Theory in Generalized Metric Spaces Book PDF

Author : Erdal Karapinar,Ravi P. Agarwal
Publisher : Springer Nature
Page : 141 pages
File Size : 54,7 Mb
Release : 2022-12-07
Category : Mathematics
ISBN : 9783031149696

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Fixed Point Theory in Generalized Metric Spaces by Erdal Karapinar,Ravi P. Agarwal Pdf

This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.

Metric Fixed Point Theory

Pradip Debnath,Nabanita Konwar,Stojan Radenović
Metric Fixed Point Theory Book PDF

Author : Pradip Debnath,Nabanita Konwar,Stojan Radenović
Publisher : Springer Nature
Page : 356 pages
File Size : 48,5 Mb
Release : 2022-01-04
Category : Mathematics
ISBN : 9789811648960

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Metric Fixed Point Theory by Pradip Debnath,Nabanita Konwar,Stojan Radenović Pdf

This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. Chapters contributed by renowned researchers from across the world, this book includes several useful tools and techniques for the development of skills and expertise in the area. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces. New insight into parametric metric spaces as well as study of variational inequalities and variational control problems have been included.

Fixed Point Theory in Metric Spaces

Praveen Agarwal,Mohamed Jleli,Bessem Samet
Fixed Point Theory in Metric Spaces Book PDF

Author : Praveen Agarwal,Mohamed Jleli,Bessem Samet
Publisher : Springer
Page : 166 pages
File Size : 55,7 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.

Nonlinear Analysis

Themistocles M Rassias
Nonlinear Analysis Book PDF

Author : Themistocles M Rassias
Publisher : World Scientific
Page : 571 pages
File Size : 41,5 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 9789814513654

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Nonlinear Analysis by Themistocles M Rassias Pdf

Contents: Fixed Point Theory and Nonlinear Problems (Th Rassias)Global Linearization Iterative Methods and Nonlinear Partial Differential Equations III (M Altman)On Generalized Power Series and Generalized Operational Calculus and Its Application (M Al-Bassam)Multiple Solutions to Parametrized Nonlinear Differential Systems from Nielsen Fixed Point Theory (R Brown)The topology of Ind-Affine Sets (P Cherenack)Almost Approximately Polynomial Functions (P Cholewa)Cohomology Classes and Foliated Manifolds (M Craioveanu & M Puta)Bifurcation and Nonlinear Instability in Applied Mathematics (L Debnath)The Stability of Weakly Additive Functional (H Drljevic)Index Theory for G-Bundle Pairs with Applications to Borsuk-Ulam Type Theorems for G-Sphere Bundles (E Fadell & S Husseini)Nonlinear Approximation and Moment Problem (J S Hwang & G D Lin)Periods in Equicontinuous Topological Dynamical Systems (A Iwanik et al.)Continuation Theorems for Semi-Linear Equations in Banach Spaces: A Survey (J Mawhin & K Rybakowski)On Contractifiable Self-Mappings (P Meyers)Normal Structures and Nonexpansive Mappings in Banach Spaces (J Nelson et al.): Survey on Uniqueness and Classification Theorems for Minimal Surfaces (Th Rassias)Contractive Definitions (B Rhoades)On KY Fan's Theorem and Its Applications (S Singh)Fixed Points of Amenable Semigroups of Differentiable Operators (P Soardi)Research Problems on Nonlinear Equations (Th Rassias) Readership: Mathematicians and applied scientists. Keywords:Nonlinear Analysis;Nonlinear Partial Differential Equations III;Polynomial Functions;Cohomology Classes;Foliated Manifolds;Topological Dynamical Systems;Minimal Surfaces;Differentiable Operators;Nonlinear Equations

Fixed Point Theory in Metric Type Spaces

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

Author : Ravi P. Agarwal,Erdal KARAPINAR,Donal O’Regan,Antonio Francisco Roldán-López-de-Hierro
Publisher : Springer
Page : 385 pages
File Size : 40,5 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.

Handbook of Set-Theoretic Topology

K. Kunen,J. Vaughan
Handbook of Set Theoretic Topology Book PDF

Author : K. Kunen,J. Vaughan
Publisher : Elsevier
Page : 1282 pages
File Size : 43,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295152

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Handbook of Set-Theoretic Topology by K. Kunen,J. Vaughan Pdf

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Handbook of Metric Fixed Point Theory

W.A. Kirk,B. Sims
Handbook of Metric Fixed Point Theory Book PDF

Author : W.A. Kirk,B. Sims
Publisher : Springer Science & Business Media
Page : 702 pages
File Size : 50,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401717489

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Handbook of Metric Fixed Point Theory by W.A. Kirk,B. Sims Pdf

Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide 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.

Mathematical Analysis and Applications

Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal
Mathematical Analysis and Applications Book PDF

Author : Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal
Publisher : John Wiley & Sons
Page : 1050 pages
File Size : 45,5 Mb
Release : 2018-04-11
Category : Mathematics
ISBN : 9781119414339

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Mathematical Analysis and Applications by Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal Pdf

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Advances in Metric Fixed Point Theory and Applications

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

Author : Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro
Publisher : Springer Nature
Page : 503 pages
File Size : 55,8 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.

Fixed Point Theory in Distance Spaces

William Kirk,Naseer Shahzad
Fixed Point Theory in Distance Spaces Book PDF

Author : William Kirk,Naseer Shahzad
Publisher : Springer
Page : 173 pages
File Size : 49,7 Mb
Release : 2014-10-23
Category : Mathematics
ISBN : 9783319109275

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Fixed Point Theory in Distance Spaces by William Kirk,Naseer Shahzad Pdf

This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.

Mathematical Analysis and Applications

Themistocles M. Rassias,Panos M. Pardalos
Mathematical Analysis and Applications Book PDF

Author : Themistocles M. Rassias,Panos M. Pardalos
Publisher : Springer Nature
Page : 694 pages
File Size : 51,9 Mb
Release : 2019-12-12
Category : Mathematics
ISBN : 9783030313395

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Mathematical Analysis and Applications by Themistocles M. Rassias,Panos M. Pardalos Pdf

An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.

Current Trends in Analysis and Its Applications

Vladimir V. Mityushev,Michael V. Ruzhansky
Current Trends in Analysis and Its Applications Book PDF

Author : Vladimir V. Mityushev,Michael V. Ruzhansky
Publisher : Birkhäuser
Page : 892 pages
File Size : 51,9 Mb
Release : 2015-02-04
Category : Mathematics
ISBN : 9783319125770

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Current Trends in Analysis and Its Applications by Vladimir V. Mityushev,Michael V. Ruzhansky Pdf

This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following topics: - Differential Equations: Complex and Functional Analytic Methods - Nonlinear PDE - Qualitative Properties of Evolution Models - Differential and Difference Equations - Toeplitz Operators - Wavelet Theory - Topological and Geometrical Methods of Analysis - Queueing Theory and Performance Evaluation of Computer Networks - Clifford and Quaternion Analysis - Fixed Point Theory - M-Frame Constructions - Spaces of Differentiable Functions of Several Real Variables Generalized Functions - Analytic Methods in Complex Geometry - Topological and Geometrical Methods of Analysis - Integral Transforms and Reproducing Kernels - Didactical Approaches to Mathematical Thinking Their wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.

Fixed Point Theory and Applications

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

Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Cambridge University Press
Page : 182 pages
File Size : 45,6 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.

Fundamentals of Signal Processing in Generalized Metric Spaces

Andrey Popoff
Fundamentals of Signal Processing in Generalized Metric Spaces Book PDF

Author : Andrey Popoff
Publisher : CRC Press
Page : 839 pages
File Size : 44,7 Mb
Release : 2022-04-19
Category : Technology & Engineering
ISBN : 9781000572001

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Fundamentals of Signal Processing in Generalized Metric Spaces by Andrey Popoff Pdf

Exploring the interrelations between generalized metric spaces, lattice-ordered groups, and order statistics, the book contains a new algebraic approach to Signal Processing Theory. It describes mathematical concepts and results important in the development, analysis, and optimization of signal processing algorithms intended for various applications. The book offers a solution of large-scale Signal Processing Theory problems of increasing both signal processing efficiency under prior uncertainty conditions and signal processing rate that is provided by multiplication-free signal processing algorithms based on lattice-ordered group operations. From simple basic relationships to computer simulation, the text covers a wide range of new mathematical techniques essential for understanding the proposed signal processing algorithms developed for solving the following problems: signal parameter and spectral estimation, signal filtering, detection, classification, and resolution; array signal processing; demultiplexing and demodulation in multi-channel communication systems and multi-station networks; wavelet analysis of 1D/ 2D signals. Along with discussing mathematical aspects, each chapter presents examples illustrating operation of signal processing algorithms developed for various applications. The book helps readers understand relations between known classic and obtained results as well as recent research trends in Signal Processing Theory and its applications, providing all necessary mathematical background concerning lattice-ordered groups to prepare readers for independent work in the marked directions including more advanced research and development.