Recent Developments In Fixed Point Theory
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Recent Developments In Fixed Point Theory
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Author : Mudasir Younis
language : en
Publisher: Springer Nature
Release Date : 2024-07-03
Recent Developments In Fixed Point Theory written by Mudasir Younis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-03 with Mathematics categories.
This contributed book has a comprehensive collection of 17 carefully curated chapters that delve into the latest advancements in fixed-point theory and its diverse applications. It bridges the gap between theory and practicality, providing readers with a deep understanding of fundamental theorems related to the existence and uniqueness of maps. The book covers a wide array of applications, each showcasing the relevance of fixed-point theory in various domains. Readers will explore applications dealing with topological properties, the resolution of integral equations across multiple classes, nonlinear differential equations, fractional differential equations, dynamic programming problems, and engineering science-related challenges. This diverse range of topics ensures that the book caters to both theoretical researchers and practitioners seeking real-world solutions. The primary feature of the book is the pictorial depictions of examples, making complex concepts more accessible and understandable. These visual representations enhance the learning experience, enabling readers to grasp the enunciated outcomes effortlessly. The book stands as an essential reference for scholars, researchers, and professionals interested in the theoretical foundations and practical implications of fixed-point theory. Its blend of theoretical insights and real-world applications makes it an indispensable addition to the field of mathematics and its interdisciplinary applications.
Mathematical Analysis And Applications
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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-04-11
Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-11 with Mathematics categories.
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.
Recent Advances In Fixed Point Theory And Applications
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Author : Umesh C. Gairola
language : en
Publisher:
Release Date : 2017
Recent Advances In Fixed Point Theory And Applications written by Umesh C. Gairola and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Fixed point theory categories.
Fixed point theory is a growing and exciting branch of mathematics with a variety of wide applications in biological and mathematical sciences, proposing newer applications in discrete dynamics and super fractals. The present endeavour is to report the latest trend in metric fixed point theory, emphasising newer applications in numerical analysis, discrete dynamics and fractal graphics, besides traditional applications. The book is useful to a large class of readers interested in analysis, applicable mathematics and fractal graphics. The articles have been selected carefully so that the book is useful for sophomores up to senior researchers looking for new material and new ideas in the existence of fixed points, new applications and survey articles. A few chapters included herein are formal in nature and suggest new directions of research in this area, which are especially useful to beginners in the field. The book is divided into two parts: Part I contains surveys and existence and convergence results. In Part II (Applications), various applications of fixed point theory to initial value problems, local attractivity of certain functional integral equation solutions, fractals and super-fractals, and solving equations in numerical praxis have been discussed. The present book, which is dedicated to Professor Shyam Lal Singh, consists of articles contributed by outstanding workers all over the world. Of course, some of the articles were selected from the Symposium on Fixed Point Theory and Applications (dedicated to him) held during the 19th Annual Conference Of India (10-12 November 2016), organised by Pauri Garhwal of the Department of Mathematics, H N B Garhwal (Central) University.
Metric Fixed Point Theory
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Author : Pradip Debnath
language : en
Publisher: Springer Nature
Release Date : 2022-01-04
Metric Fixed Point Theory written by Pradip Debnath and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Mathematics categories.
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 Probabilistic Metric Spaces
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Author : O. Hadzic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fixed Point Theory In Probabilistic Metric Spaces written by O. Hadzic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.
Theory And Application Of Fixed Point
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Author : Erdal Karapinar
language : en
Publisher: Mdpi AG
Release Date : 2021-09-30
Theory And Application Of Fixed Point written by Erdal Karapinar and has been published by Mdpi AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-30 with Mathematics categories.
In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.
Metric Structures And Fixed Point Theory
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Author : Dhananjay Gopal
language : en
Publisher: CRC Press
Release Date : 2021-04-08
Metric Structures And Fixed Point Theory written by Dhananjay Gopal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-08 with Mathematics categories.
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.
Background And Recent Developments Of Metric Fixed Point Theory
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Author : Dhananjay Gopal
language : en
Publisher: CRC Press
Release Date : 2017-11-28
Background And Recent Developments Of Metric Fixed Point Theory written by Dhananjay Gopal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Mathematics categories.
This book focusing on Metric fixed point theory is designed to provide an extensive understanding of the topic with the latest updates. It provides a good source of references, open questions and new approaches. While the book is principally addressed to graduate students, it is also intended to be useful to mathematicians, both pure and applied.
Fixed Point Theory And Applications
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Author : Ravi P. Agarwal
language : en
Publisher: Cambridge University Press
Release Date : 2001-03-22
Fixed Point Theory And Applications written by Ravi P. Agarwal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-22 with Mathematics categories.
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.
Fixed Point Theory In P Vector Spaces
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Author : George Xianzhi Yuan
language : en
Publisher: World Scientific
Release Date : 2025-05-05
Fixed Point Theory In P Vector Spaces written by George Xianzhi Yuan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.
This monograph provides an updated development of fixed point theory under a unified framework of the 'best approximation approach' in p-vector spaces, a core component of nonlinear analysis in mathematics, where p∊(0,1] (the same for p below unless specified). This book exposes some important contents of the new fixed point theory, with highlights in four parts.Specifically, the book focuses on the development of general new fixed point theory for both single-valued and set-valued mappings under the framework of p-vector and locally convex spaces for p∊(0,1], including topological vector spaces and locally convex spaces as special cases. It provides affirmative answers to the Schauder conjecture under the general setting of p-vector spaces and locally p-convex spaces. The book establishes best approximation results for upper semicontinuous and 1-set contractive set-valued mappings, which are used as tools to establish new fixed point theorems for non-self set-valued mappings with either inward or outward set conditions under various situations. These results improve or unify corresponding results in the existing literature for nonlinear analysis and lay the foundation for the development of fixed point theorems in topological vector spaces since Schauder's conjecture was raised in 1930. In addition, this book demonstrates the power of the fixed point theorem by showing the equivalence among the Ekeland variational principle, Takahashi minimization theorem, Oettli-Théra theorem, Caristi-Kirk type fixed point theorem, and related principles in nonlinear functional analysis.Overall, this book provides an accessible way to establish the new theory in the development of fixed point theorems and results. It is designed to be understandable for senior undergraduate students majoring in mathematics, physical sciences, social sciences, and related fields. We expect that this monograph will serve as a staple textbook for undergraduate and postgraduate students, a reference book for researchers in the field of fixed point theory in nonlinear functional analysis, and an accessible resource for general readers in mathematics and related disciplines.