Fixed Point Theory For Non Self Weakly Contractive Mappings Defined Implicitly Using Multiplicative C Class Functions
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| Author | : Clement Ampadu |
| Publisher | : Lulu.com |
| Total Pages | : 44 |
| Release | : 2017-06-11 |
| Genre | : Science |
| ISBN | : 1387011952 |
In this monograph we have defined the non-self multiplicative version of weakly contractive maps implicitly via the multiplicative C-class and obtained some sufficient conditions that assure the existence and/or uniqueness of the best proximity point in the multiplicative analogue of Metric space, S-Metric Space, and Metric space with Partial Order.
| Author | : Clement Ampadu |
| Publisher | : Lulu.com |
| Total Pages | : 41 |
| Release | : 2017-05-08 |
| Genre | : Science |
| ISBN | : 1365924432 |
In this monograph we have defined the multiplicative version of weakly contractive mappings implicitly via the multiplicative C-class function and obtained some fixed point theorems for such mappings in the multiplicative analogue of various spaces. A nice feature of this monograph are the (publishable) exercise set, which begs the reader to explore the beautiful connection between weakly contractive mappings, c-class function, and their multiplicative analogue.
| Author | : Clement Ampadu |
| Publisher | : Lulu.com |
| Total Pages | : 42 |
| Release | : 2017-07-11 |
| Genre | : Science |
| ISBN | : 1387066110 |
We examine the connection between the cyclical extension of weakly contractive maps and C-class functions in the multiplicative analogue of Metric space and Partial metric space.
| Author | : Vittorino Pata |
| Publisher | : Springer Nature |
| Total Pages | : 171 |
| Release | : 2019-09-22 |
| Genre | : Mathematics |
| ISBN | : 3030196704 |
This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.
| Author | : W.A. Kirk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 702 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401717486 |
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.
| Author | : Anita Tomar |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2021 |
| Genre | : Fixed point theory |
| ISBN | : 9781536193367 |
"Fixed-point theory initially emerged in the article demonstrating existence of solutions of differential equations, which appeared in the second quarter of the 18th century (Joseph Liouville, 1837). Later on, this technique was improved as a method of successive approximations (Charles Emile Picard, 1890) which was extracted and abstracted as a fixed-point theorem in the framework of complete normed space (Stefan Banach, 1922). It ensures presence as well as uniqueness of a fixed point, gives an approximate technique to really locate the fixed point and the a priori and a posteriori estimates for the rate of convergence. It is an essential device in the theory of metric spaces. Subsequently, it is stated that fixed-point theory is initiated by Stefan Banach. Fixed-point theorems give adequate conditions under which there exists a fixed point for a given function and enable us to ensure the existence of a solution of the original problem. In an extensive variety of scientific issues, beginning from different branches of mathematics, the existence of a solution is comparable to the existence of a fixed point for a suitable mapping. The book "Fixed Point Theory & its Applications to Real World Problems" is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further exploration and makes for an easily accessible source of knowledge. This book is apposite for young researchers who want to pursue their research in fixed-point theory and is the latest in the field, giving new techniques for the existence of a superior fixed point, a fixed point, a near fixed point, a fixed circle, a near fixed interval circle, a fixed disc, a near fixed interval disc, a coincidence point, a common fixed point, a coupled common fixed point, amiable fixed sets, strong coupled fixed points and so on, utilizing minimal conditions. It offers novel applications besides traditional applications which are applicable to real world problems. The book is self-contained and unified which will serve as a reference book to researchers who are in search of novel ideas. It will be a valued addition to the library"--
| Author | : Lynn Harold Loomis |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 595 |
| Release | : 2014-02-26 |
| Genre | : Mathematics |
| ISBN | : 9814583952 |
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
| Author | : Monther Alfuraidan |
| Publisher | : Academic Press |
| Total Pages | : 444 |
| Release | : 2016-06-20 |
| Genre | : Mathematics |
| ISBN | : 0128043652 |
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 | : Haim Brezis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 600 |
| Release | : 2010-11-02 |
| Genre | : Mathematics |
| ISBN | : 0387709142 |
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
| Author | : Ravi P. Agarwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2009-06-12 |
| Genre | : Mathematics |
| ISBN | : 0387758186 |
In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis. This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields. This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.
