Iterative Approximation Of Fixed Points In Hilbert Spaces
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Iterative Approximation Of Fixed Points
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Author : Vasile Berinde
language : en
Publisher: Springer
Release Date : 2007-04-20
Iterative Approximation Of Fixed Points written by Vasile Berinde and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-20 with Mathematics categories.
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.
Iterative Methods For Fixed Point Problems In Hilbert Spaces
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Author : Andrzej Cegielski
language : en
Publisher: Springer
Release Date : 2012-09-14
Iterative Methods For Fixed Point Problems In Hilbert Spaces written by Andrzej Cegielski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
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.
Iterative Approximation Of Fixed Points In Hilbert Spaces
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Author : Iyiola Olaniyi
language : de
Publisher: LAP Lambert Academic Publishing
Release Date : 2012-07
Iterative Approximation Of Fixed Points In Hilbert Spaces written by Iyiola Olaniyi and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07 with categories.
Functional Analysis, Fixed Points Theory and Iterative Schemes are key areas of research in Mathematics today. This work introduces the readers to introductory part of functional analysis, fixed points theory and some iterative schemes and applications in solving differential equations. It is interesting to see how the iterative schemes work in obtaining solutions to initial value problems. Several maps of interest are explained and their relationship given concrete examples to illustrate the idea. Much attention is given to a special class of problems in non-linear functional analysis namely: iterative approximation of k-strictly pseudo-contractive maps in Hilbert spaces using Modified Picard Iteration.
Fixed Point Theory Variational Analysis And Optimization
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Author : Saleh Abdullah R. Al-Mezel
language : en
Publisher: CRC Press
Release Date : 2014-06-03
Fixed Point Theory Variational Analysis And Optimization written by Saleh Abdullah R. Al-Mezel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-03 with Business & Economics categories.
Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis-fixed point theory, variational inequalities, and vector optimization-but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions invol
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.
Topics In Fixed Point Theory
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Author : Saleh Almezel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-23
Topics In Fixed Point Theory written by Saleh Almezel 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 2013-10-23 with Mathematics categories.
The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents 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. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.
Fixed Points Of Nonlinear Operators
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Author : Haiyun Zhou
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-06-08
Fixed Points Of Nonlinear Operators written by Haiyun Zhou and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-08 with Mathematics categories.
Iterative Methods for Fixed Points of Nonlinear Operators offers an introduction into iterative methods of fixed points for nonexpansive mappings, pseudo-contrations in Hilbert Spaces and in Banach Spaces. Iterative methods of zeros for accretive mappings in Banach Spaces and monotone mappings in Hilbert Spaces are also discussed. It is an essential work for mathematicians and graduate students in nonlinear analysis.
Nonlinear Analysis Geometry And Applications
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Author : Diaraf Seck
language : en
Publisher: Springer Nature
Release Date : 2024-05-22
Nonlinear Analysis Geometry And Applications written by Diaraf Seck and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-22 with Mathematics categories.
The NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed. This book features the best papers presented during this Biennial. The different topics addressed are related to Partial Differential Equations, Differential inclusions, Geometrical Analysis of Optimal Shapes, Complex Analysis, Geometric Structures, Algebraic Geometry, Algebraic, Optimization, Optimal Control and Mathematical modeling. The main focus of the NLAGA project is to deepen and consolidate the development in West and Center Africa of Nonlinear Analysis, Geometry and their Applications, aimed at solving in particular real-world problems such as coastal erosion, urban network, pollution problems, and population dynamics.
Fixed Point Algorithms For Inverse Problems In Science And Engineering
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Author : Heinz H. Bauschke
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
Fixed Point Algorithms For Inverse Problems In Science And Engineering written by Heinz H. Bauschke 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 2011-05-27 with Mathematics categories.
"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
Geometric Properties Of Banach Spaces And Nonlinear Iterations
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Author : Charles Chidume
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-27
Geometric Properties Of Banach Spaces And Nonlinear Iterations written by Charles Chidume 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 2009-03-27 with Mathematics categories.
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.