# Convex and Set-Valued Analysis: Selected Topics - De Gruyter Textbook (Paperback)

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Paperback 209 Pages / Published: 05/12/2016
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This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents: Preface Part I: Convex analysis Convex sets and their properties The convex hull of a set. The interior of convex sets The affine hull of sets. The relative interior of convex sets Separation theorems for convex sets Convex functions Closedness, boundedness, continuity, and Lipschitz property of convex functions Conjugate functions Support functions Differentiability of convex functions and the subdifferential Convex cones A little more about convex cones in infinite-dimensional spaces A problem of linear programming More about convex sets and convex hulls Part II: Set-valued analysis Introduction to the theory of topological and metric spaces The Hausdorff metric and the distance between sets Some fine properties of the Hausdorff metric Set-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps A base of topology of the spaceHc(X) Measurable set-valued maps. Measurable selections and measurable choice theorems The superposition set-valued operator The Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations Special selections of set-valued maps Differential inclusions Fixed points and coincidences of maps in metric spaces Stability of coincidence points and properties of covering maps Topological degree and fixed points of set-valued maps in Banach spaces Existence results for differential inclusions via the fixed point method Notation Bibliography Index

Publisher: De Gruyter
ISBN: 9783110460285
Number of pages: 209
Weight: 410 g
Dimensions: 240 x 170 x 13 mm

MEDIA REVIEWS

"Written by two experts in these areas and based on their teaching experience, the book contains a clear and accessible introduction to convex and set-valued analysis. It can be used for courses on these topics or for self-study."
Adrian Petrusel in: Stud. Univ. Babes-Bolyai Math. 62(2017), No. 1, 137-138

"Das Buch enth lt eine kompakte und moderne Darstellung wichtiger Aspekte sowohl der konvexen als auch der mengen-wertigen konvexen Analysis. Es schlie t sich ideal an die in Grundvorlesungen der Analysis und Funktionalanalysis behandelten Themen an, vertieft diese und ist f r Seminare im Masterstudium sehr geeignet."
Seniorprof. Martin Weber, TU Dresden

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