Convergence Theorems for Berinde Type Non-Expansive Mappings PDF Download

Author: Clement Ampadu
Publisher: Lulu.com
ISBN: 1387395750
Category : Science
Languages : en
Pages : 50

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Book Description
We examine the relationship between total asymptotically nonexpansive mappings, I-asymptotically quasi-nonexpansive mappings, nonself asymptotically I-nonexpansive mappings; nonself asymptotically nonexpansive mappings, which are inspired by when the Banach contraction is nonexpansive, with respect to when a certain Berinde-type contraction is nonexpansive

Author: Vasile Berinde
Publisher: Springer
ISBN: 3540722343
Category : Mathematics
Languages : en
Pages : 338

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Book Description
This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Author: Charles Chidume
Publisher: Springer Science & Business Media
ISBN: 1848821891
Category : Mathematics
Languages : en
Pages : 337

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Book Description
The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 756

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Author: Michael Ruzhansky
Publisher: Birkhäuser
ISBN: 981104337X
Category : Mathematics
Languages : en
Pages : 304

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Book Description
This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them with a number of solved examples. The topics include real and complex analysis, special functions and analytic number theory, q-series, Ramanujan’s mathematics, fractional calculus, Clifford and harmonic analysis, graph theory, complex analysis, complex dynamical systems, complex function spaces and operator theory, geometric analysis of complex manifolds, geometric function theory, Riemannian surfaces, Teichmüller spaces and Kleinian groups, engineering applications of complex analytic methods, nonlinear analysis, inequality theory, potential theory, partial differential equations, numerical analysis , fixed-point theory, variational inequality, equilibrium problems, optimization problems, stability of functional equations, and mathematical physics. It includes papers presented at the 24th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (24ICFIDCAA), held at the Anand International College of Engineering, Jaipur, 22–26 August 2016. The book is a valuable resource for researchers in real and complex analysis.

Author: Nurwati Djam'an
Publisher: Springer Nature
ISBN: 9464633328
Category : Mathematics
Languages : en
Pages : 237

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Book Description
This is an open access book. There are still many other problems occur within the development of the science and frequently implemented that must be answered and discussed intensively to protect sacred goals of the science. Academic ambiance and spirits have to be returned as challenges keeps interfering within this digital development of the society. By this condition, the conference is an important step and expected to be a comprehensive pace in aligning various scientific problems and interests as the consequence of 5.0 era of society. International Conference on Statistics, Mathematics, Teaching, and Research (ICSMTR) 2023 is a conference for those who are interested in presenting papers in all fields of mathematics and statistics. This conference is a forum for discussion between various parties such as academicians, policy makers and social practitioners.

Author: Monther Alfuraidan
Publisher: Academic Press
ISBN: 0128043652
Category : Mathematics
Languages : en
Pages : 444

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Book Description
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: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 0387758186
Category : Mathematics
Languages : en
Pages : 373

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Book Description
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.

Author: Diaraf Seck
Publisher: Springer Nature
ISBN: 3031526813
Category :
Languages : en
Pages : 410

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Author: Andrzej Cegielski
Publisher: Springer
ISBN: 3642309011
Category : Mathematics
Languages : en
Pages : 312

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Book Description
Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.