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Titlebook: Geometric Properties of Banach Spaces and Nonlinear Iterations; Charles Chidume Book 2009 Springer-Verlag London 2009 45XX.46XX.47XX.49XX.

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发表于 2025-3-21 19:46:20 | 显示全部楼层 |阅读模式
书目名称Geometric Properties of Banach Spaces and Nonlinear Iterations
编辑Charles Chidume
视频videohttp://file.papertrans.cn/384/383597/383597.mp4
概述Self-contained, with detailed motivations, explanations and examples.In-depth, comprehensive and up-to-date coverage.Contains interesting, important and reasonable open problems.Summaries of key inequ
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Geometric Properties of Banach Spaces and Nonlinear Iterations; Charles Chidume Book 2009 Springer-Verlag London 2009 45XX.46XX.47XX.49XX.
描述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, “...
出版日期Book 2009
关键词45XX; 46XX; 47XX; 49XX; 65XX; 68XX; Convexity; Families of operators; Hammerstein equations; Iterative method
版次1
doihttps://doi.org/10.1007/978-1-84882-190-3
isbn_softcover978-1-84882-189-7
isbn_ebook978-1-84882-190-3Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag London 2009
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Combined Analog Digital Integration: CANDI. : . → . is Lipschitz, then, by Schauder fixed point theorem, . has a fixed point in .. All efforts to approximate such a fixed point by means of the Mann sequence when . is also assumed to be pseudo-contractive proved abortive. In 1974, Ishikawa introduced a new iteration scheme and proved the following theorem.
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Arthroscopic Capsulolabral Repair,re general than Hilbert spaces. However, two other iteration methods have been introduced and have successfully been employed to approximate fixed points of Lipschitz pseudo-contractive mappings in certain Banach spaces ..
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The Medial Patellofemoral Ligamentbeen flourishing areas of research for many mathematicians. For the classes of mappings mentioned here in (.) to (.), we show in this chapter that modifications of the Mann iteration algorithm and of the Halpern-type iteration process studied in chapter 6 can be used to approximate fixed points (when they exist).
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Basic Concepts in Hip Arthroscopy,lt of Markov is more general than this but this version is adequate for our purposes)..Motivated by this result, De Marr studied the problem of the existence of a common fixed point for a family of . maps, and proved the following theorem.
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Some Geometric Properties of Banach Spaces,pter 2, we shall introduce the class of .. All the results presented in these two chapters are well-known and standard and can be found in several books on geometry of Banach spaces, for example, in Diestel [206], or in Lindenstrauss and Tzafriri [312]. Consequently, we shall skip some details and long proofs.
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