Geometry of Linear 2-normed Spaces
Author: Raymond W. Freese
Publisher: Nova Publishers
Published: 2001
Total Pages: 314
ISBN-13: 9781590330197
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Author: Raymond W. Freese
Publisher: Nova Publishers
Published: 2001
Total Pages: 314
ISBN-13: 9781590330197
DOWNLOAD EBOOKAuthor: Charles Chidume
Publisher: Springer Science & Business Media
Published: 2009-03-27
Total Pages: 337
ISBN-13: 1848821891
DOWNLOAD EBOOKThe 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: Mahlon M. Day
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 222
ISBN-13: 3662090007
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Publisher: Elsevier
Published: 2001-08-15
Total Pages: 1017
ISBN-13: 0080532802
DOWNLOAD EBOOKThe 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.
Author:
Publisher: Elsevier
Published: 2011-10-10
Total Pages: 321
ISBN-13: 0080871798
DOWNLOAD EBOOKIntroduction to Banach Spaces and their Geometry
Author: L. M. Kelly
Publisher: Springer
Published: 2006-11-14
Total Pages: 257
ISBN-13: 3540379460
DOWNLOAD EBOOKAuthor: D. Jude Hemanth
Publisher: Springer Nature
Published: 2020-01-03
Total Pages: 1105
ISBN-13: 3030361780
DOWNLOAD EBOOKThis book features research presented at the 1st International Conference on Artificial Intelligence and Applied Mathematics in Engineering, held on 20–22 April 2019 at Antalya, Manavgat (Turkey). In today’s world, various engineering areas are essential components of technological innovations and effective real-world solutions for a better future. In this context, the book focuses on problems in engineering and discusses research using artificial intelligence and applied mathematics. Intended for scientists, experts, M.Sc. and Ph.D. students, postdocs and anyone interested in the subjects covered, the book can also be used as a reference resource for courses related to artificial intelligence and applied mathematics.
Author: Gilles Pisier
Publisher: Cambridge University Press
Published: 1999-05-27
Total Pages: 270
ISBN-13: 9780521666350
DOWNLOAD EBOOKA self-contained presentation of results relating the volume of convex bodies and Banach space geometry.
Author: Margaret Ann Tevis Herzog
Publisher:
Published: 1959
Total Pages: 62
ISBN-13:
DOWNLOAD EBOOKAuthor: Robert Gardner Bartle
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 186
ISBN-13: 0821850571
DOWNLOAD EBOOKFeatures 17 papers that resulted from a 1983 conference held to honor Professor Mahlon Marsh Day upon his retirement from the University of Illinois. This work is suitable for researchers and graduate students in functional analysis.