From Hahn Banach To Monotonicity
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From Hahn Banach To Monotonicity
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Author : Stephen Simons
language : en
Publisher: Springer
Release Date : 2008-02-22
From Hahn Banach To Monotonicity written by Stephen Simons and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-22 with Mathematics categories.
This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique" for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.
From Hahn Banach To Monotonicity
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Author : Stephen Simons
language : en
Publisher: Springer
Release Date : 2009-09-03
From Hahn Banach To Monotonicity written by Stephen Simons and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Mathematics categories.
This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique" for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.
Minimax And Monotonicity
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Author : Stephen Simons
language : en
Publisher: Springer
Release Date : 2006-11-14
Minimax And Monotonicity written by Stephen Simons and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.
From Hahn Banach To Monotonicity
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Author : Stephen Simons
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-13
From Hahn Banach To Monotonicity written by Stephen Simons 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 2008-02-13 with Mathematics categories.
This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique" for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.
Nonlinear Analysis
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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-02
Nonlinear Analysis written by Panos M. Pardalos 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 2012-06-02 with Mathematics categories.
The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.
Geometry Of Banach Spaces Duality Mappings And Nonlinear Problems
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Author : I. Cioranescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry Of Banach Spaces Duality Mappings And Nonlinear Problems written by I. Cioranescu 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 2012-12-06 with Mathematics categories.
One service mathematics has rendered the 'Et moi ... - si Javait so comment en revenir. je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. AIl arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Convex Analysis And Monotone Operator Theory In Hilbert Spaces
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Author : Heinz H. Bauschke
language : en
Publisher: Springer
Release Date : 2017-02-28
Convex Analysis And Monotone Operator Theory In Hilbert Spaces written by Heinz H. Bauschke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-28 with Mathematics categories.
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Infinite Products Of Operators And Their Applications
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Author : Simeon Reich
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-03-30
Infinite Products Of Operators And Their Applications written by Simeon Reich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-30 with Mathematics categories.
This volume contains the proceedings of the workshop on Infinite Products of Operators and Their Applications, held from May 21-24, 2012, at the Technion-Israel Institute of Technology, Haifa, Israel. The papers cover many different topics regarding infinite products of operators and their applications: projection methods for solving feasibility and best approximation problems, arbitrarily slow convergence of sequences of linear operators, monotone operators, proximal point algorithms for finding zeros of maximal monotone operators in the presence of computational errors, the Pascoletti-Serafini problem, remetrization for infinite families of mappings, Poisson's equation for mean ergodic operators, vector-valued metrics in fixed point theory, contractivity of infinite products and mean convergence theorems for generalized nonspreading mappings. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel).
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.
Sequence Space Theory With Applications
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Author : S. A. Mohiuddine
language : en
Publisher: CRC Press
Release Date : 2022-07-20
Sequence Space Theory With Applications written by S. A. Mohiuddine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-20 with Mathematics categories.
The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications. Features Discusses the Fibonacci and vector valued difference sequence spaces Presents the solution of Volterra integral equation in Banach algebra Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix Presents the Tauberian theorems of double sequences Discusses the paranormed Riesz difference sequence space of fractional order Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.