Geometry Of Linear 2 Normed Spaces
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Geometry Of Linear 2 Normed Spaces
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Author : Raymond W. Freese
language : en
Publisher: Nova Publishers
Release Date : 2001
Geometry Of Linear 2 Normed Spaces written by Raymond W. Freese and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Normed Linear Spaces
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Author : Mahlon M. Day
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Normed Linear Spaces written by Mahlon M. Day 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 2013-03-14 with Mathematics categories.
Classical Analysis On Normed Spaces
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Author : Tsoy-Wo Ma
language : en
Publisher: World Scientific
Release Date : 1995
Classical Analysis On Normed Spaces written by Tsoy-Wo Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis.
Handbook Of The Geometry Of Banach Spaces
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Author :
language : en
Publisher: Elsevier
Release Date : 2001-08-15
Handbook Of The Geometry Of Banach Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-15 with Mathematics categories.
The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
The Geometry Of Metric And Linear Spaces
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Author : L. M. Kelly
language : en
Publisher: Springer
Release Date : 2006-11-14
The Geometry Of Metric And Linear Spaces written by L. M. Kelly 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.
Geometry Of Normed Linear Spaces
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Author : R. G. Birtle
language : en
Publisher:
Release Date : 1986
Geometry Of Normed Linear Spaces written by R. G. Birtle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Norm Derivatives And Characterizations Of Inner Product Spaces
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Author : Claudi Alsina
language : en
Publisher: World Scientific
Release Date : 2010
Norm Derivatives And Characterizations Of Inner Product Spaces written by Claudi Alsina and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. Introduction. 1.1. Historical notes. 1.2. Normed linear spaces. 1.3. Strictly convex normed linear spaces. 1.4. Inner product spaces. 1.5. Orthogonalities in normed linear spaces -- 2. Norm derivatives. 2.1. Norm derivatives : Definition and basic properties. 2.2. Orthogonality relations based on norm derivatives. 2.3. p'[symbol]-orthogonal transformations. 2.4. On the equivalence of two norm derivatives. 2.5. Norm derivatives and projections in normed linear spaces. 2.6. Norm derivatives and Lagrange's identity in normed linear spaces. 2.7. On some extensions of the norm derivatives. 2.8. p-orthogonal additivity -- 3. Norm derivatives and heights. 3.1. Definition and basic properties. 3.2. Characterizations of inner product spaces involving geometrical properties of a height in a triangle. 3.3. Height functions and classical orthogonalities. 3.4. A new orthogonality relation. 3.5. Orthocenters. 3.6. A characterization of inner product spaces involving an isosceles trapezoid property. 3.7. Functional equations of the height transform -- 4. Perpendicular bisectors in Normed spaces. 4.1. Definitions and basic properties. 4.2. A new orthogonality relation. 4.3. Relations between perpendicular bisectors and classical orthogonalities. 4.4. On the radius of the circumscribed circumference of a triangle. 4.5. Circumcenters in a triangle. 4.6. Euler line in real normed space. 4.7. Functional equation of the perpendicular bisector transform -- 5. Bisectrices in real Normed spaces. 5.1. Bisectrices in real normed spaces. 5.2. A new orthogonality relation. 5.3. Functional equation of the bisectrix transform. 5.4. Generalized bisectrices in strictly convex real normed spaces. 5.5. Incenters and generalized bisectrices -- 6. Areas of triangles in Normed spaces. 6.1. Definition of four areas of triangles. 6.2. Classical properties of the areas and characterizations of inner product spaces. 6.3. Equalities between different area functions. 6.4. The area orthogonality.
Probabilistic Normed Spaces
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Author : Bernardo Lafuerza Guillén
language : en
Publisher:
Release Date : 2014-09-09
Probabilistic Normed Spaces written by Bernardo Lafuerza Guillén and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-09 with MATHEMATICS categories.
This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-date and thorough investigation of the properties, uses and applications of PN spaces, based on the standard definition. Topics covered include:: What are PN spaces?; The topology of PN spaces; Probabilistic norms and convergence; Products and quotients of PN spaces; D -boundedness and D -compactness; Normability; Invariant and semi-invariant PN spaces; Linear operators; Stability of some functional equations in PN spaces; Menger''s 2-probabilistic normed spaces . The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations. This introduction will therefore have broad relevance across mathematical and statistical research, especially those working in probabilistic functional analysis and probabilistic geometry. Contents: Preliminaries; Probabilistic Normed Spaces; The Topology of PN Spaces; Probabilistic Norms and Convergence; Products and Quotients of PN Spaces; D -Boundedness and D -Compactness; Normability; Invariant and Semi-Invariant PN Spaces; Linear Operators; Stability of Some Functional Equations in PN Spaces; Menger''s 2-Probabilistic Normed Spaces. Readership: Post graduate students and researchers in the field of Probabilistic Normed Spaces. Key Features: The theory of PN spaces is relevant as a generalization of deterministic results of linear normed spaces and also in the study of random operator equations; Deals with all the developed ideas in PN spaces; A good reference book for post graduate students and researchers in this field as it identifies the developments and open problems in PN spaces
Normed Linear Spaces
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Author : Mahlon M. Day
language : en
Publisher: Springer
Release Date : 2013-12-01
Normed Linear Spaces written by Mahlon M. Day and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.