Metric Modular Spaces
Metric Modular Spaces

Author: Vyacheslav Chistyakov

Publisher: Springer

Published: 2015-12-14

Total Pages: 148

ISBN-13: 3319252836

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Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existence of solutions to ordinary differential equations in Banach spaces with rapidly varying right-hand sides.

Metric Structures and Fixed Point Theory
Metric Structures and Fixed Point Theory

Author: Dhananjay Gopal

Publisher: CRC Press

Published: 2021-04-08

Total Pages: 317

ISBN-13: 1000366391

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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. Features Explores the latest research and developments in fixed point theory on the most popular generalizations of metric spaces 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. 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.

Metric Spaces of Fuzzy Sets
Metric Spaces of Fuzzy Sets

Author: Phil Diamond

Publisher: World Scientific

Published: 1994

Total Pages: 192

ISBN-13: 9789810217310

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The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.

Metric Fixed Point Theory
Metric Fixed Point Theory

Author: Pradip Debnath

Publisher: Springer Nature

Published: 2022-01-04

Total Pages: 356

ISBN-13: 9811648964

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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.

Optimization, Control, and Applications in the Information Age
Optimization, Control, and Applications in the Information Age

Author: Athanasios Migdalas

Publisher: Springer

Published: 2015-07-30

Total Pages: 427

ISBN-13: 3319185675

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Recent developments in theory, algorithms, and applications in optimization and control are discussed in this proceedings, based on selected talks from the ‘Optimization Control and Applications in the Information Age’ conference, organized in honor of Panos Pardalos’s 60th birthday. This volume contains numerous applications to optimal decision making in energy production and fuel management, data mining, logistics, supply chain management, market network analysis, risk analysis, and community network analysis. In addition, a short biography is included describing Dr. Pardalos’s path from a shepherd village on the high mountains of Thessaly to academic success. Due to the wide range of topics such as global optimization, combinatorial optimization, game theory, stochastics and programming contained in this publication, scientists, researchers, and students in optimization, operations research, analytics, mathematics and computer science will be interested in this volume.

Models, Algorithms, and Technologies for Network Analysis
Models, Algorithms, and Technologies for Network Analysis

Author: Boris I. Goldengorin

Publisher: Springer Science & Business Media

Published: 2012-12-12

Total Pages: 244

ISBN-13: 146145574X

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​​ ​Network Analysis has become a major research topic over the last several years. The broad range of applications that can be described and analyzed by means of a network is bringing together researchers, practitioners and other scientific communities from numerous fields such as Operations Research, Computer Science, Transportation, Energy, Social Sciences, and more. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The purpose of these proceedings is to overcome this difficulty by collecting the major results found by the participants of the “First International Conference in Network Analysis,” held at The University of Florida, Gainesville, USA, from the 14th to the 16th of December 2011. The contributions of this conference not only come from different fields, but also cover a broad range of topics relevant to the theory and practice of network analysis, including the reliability of complex networks, software, theory, methodology and applications.

Dynamical Systems
Dynamical Systems

Author: Mahmut Reyhanoglu

Publisher: BoD – Books on Demand

Published: 2017-03-15

Total Pages: 276

ISBN-13: 9535130153

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There has been a considerable progress made during the recent past on mathematical techniques for studying dynamical systems that arise in science and engineering. This progress has been, to a large extent, due to our increasing ability to mathematically model physical processes and to analyze and solve them, both analytically and numerically. With its eleven chapters, this book brings together important contributions from renowned international researchers to provide an excellent survey of recent advances in dynamical systems theory and applications. The first section consists of seven chapters that focus on analytical techniques, while the next section is composed of four chapters that center on computational techniques.

Metric Spaces
Metric Spaces

Author: E. T. Copson

Publisher: CUP Archive

Published: 1988-02-11

Total Pages: 156

ISBN-13: 9780521357326

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Professor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.

Fixed Point Theory in Modular Function Spaces
Fixed Point Theory in Modular Function Spaces

Author: Mohamed A. Khamsi

Publisher: Birkhäuser

Published: 2015-03-24

Total Pages: 251

ISBN-13: 3319140515

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This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable. The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.​

Fixed Point Theory in Distance Spaces
Fixed Point Theory in Distance Spaces

Author: William Kirk

Publisher: Springer

Published: 2014-10-23

Total Pages: 176

ISBN-13: 3319109278

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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.