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Titlebook: Variational Analysis of Regular Mappings; Theory and Applicati Alexander D. Ioffe Book 2017 Springer International Publishing AG 2017 metri

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发表于 2025-3-21 19:52:45 | 显示全部楼层 |阅读模式
书目名称Variational Analysis of Regular Mappings
副标题Theory and Applicati
编辑Alexander D. Ioffe
视频video
概述Presents a detailed study of regularity properties of mappings in metric spaces.Covers mappings with specific structures in Banach and finite dimensional spaces.Offers new and previously unrecorded ap
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Variational Analysis of Regular Mappings; Theory and Applicati Alexander D. Ioffe Book 2017 Springer International Publishing AG 2017 metri
描述.This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory...The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected ap
出版日期Book 2017
关键词metric regularity error bound; perturbation stability analysis; perturbation theory stability; set-valu
版次1
doihttps://doi.org/10.1007/978-3-319-64277-2
isbn_softcover978-3-319-87761-7
isbn_ebook978-3-319-64277-2Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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Metric Theory: Phenomenology,In this chapter we, roughly speaking, translate some principal results of the classical theory presented in the preceding chapter into purely metric language in which the key word is “distance” and words like “derivative” or “tangent space” make little sense.
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Subdifferentials: A Short Introduction,This is a service chapter. Here we shall build a new technical machinery to work with regularity problems for mappings between Banach spaces.
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Banach Space Theory: Special Classes of Mappings,If additional information on the structure of a mapping is available, it is often possible to get stronger results and/or better estimates for regularity rates and to develop more convenient mechanisms to compute or estimate the latter. In this chapter we consider several important classes of mappings for which this program can be implemented.
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Applications to Analysis and Optimization 1,In this chapter we consider applications of regularity theory to a variety of (mainly infinite-dimensional) problems of analysis and optimization.
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