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Convex and Set-Valued Analysis

Selected Topics

Aram V. Arutyunov, Valeri Obukhovskii (Autoren)

Buch | Softcover

VIII, 201 Seiten

2016
De Gruyter (Verlag)
978-3-11-046028-5 (ISBN)

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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:PrefacePart I: Convex analysisConvex sets and their propertiesThe convex hull of a set. The interior of convex setsThe affine hull of sets. The relative interior of convex setsSeparation theorems for convex setsConvex functionsClosedness, boundedness, continuity, and Lipschitz property of convex functionsConjugate functionsSupport functionsDifferentiability of convex functions and the subdifferentialConvex conesA little more about convex cones in infinite-dimensional spacesA problem of linear programmingMore about convex sets and convex hullsPart II: Set-valued analysisIntroduction to the theory of topological and metric spacesThe Hausdorff metric and the distance between setsSome fine properties of the Hausdorff metricSet-valued maps. Upper semicontinuous and lower semicontinuous set-valued mapsA base of topology of the spaceHc(X)Measurable set-valued maps. Measurable selections and measurable choice theoremsThe superposition set-valued operatorThe Michael theorem and continuous selections. Lipschitz selections. Single-valued approximationsSpecial selections of set-valued mapsDifferential inclusionsFixed points and coincidences of maps in metric spacesStability of coincidence points and properties of covering mapsTopological degree and fixed points of set-valued maps in Banach spacesExistence results for differential inclusions via the fixed point methodNotationBibliographyIndex

Aram Arutyunov, Moscow, Russia.Valerii Obukhovskii, Voronezh, Russia.

"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 enthält eine kompakte und moderne Darstellung wichtiger Aspekte sowohl der konvexen als auch der mengen-wertigen konvexen Analysis. Es schließt sich ideal an die in Grundvorlesungen der Analysis und Funktionalanalysis behandelten Themen an, vertieft diese und ist für Seminare im Masterstudium sehr geeignet."
Seniorprof. Martin Weber, TU Dresden

Erscheinungsdatum	06.12.2016
Reihe/Serie	De Gruyter Textbook
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	413 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Abbildung • Analysis • BROSCH • Convex sets • differential inclusions • Funktion • GHB • Grundlagen • Hausdorff measures • Kriminologie • Mathematical Analysis • Mathematics • Mathematik • nicht rabattbeschränkt/Sortimentstitel • Optimierung • Optimization • Schneider • Set-valued maps • Topological Spaces
ISBN-10	3-11-046028-9 / 3110460289
ISBN-13	978-3-11-046028-5 / 9783110460285
Zustand	Neuware