{"product_id":"9783110460285","title":"Convex and Set-Valued Analysis : Selected Topics (De Gruyter Textbook)","description":"\u003cp\u003eThis 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. \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eContents:\n\u003c\/strong\u003ePreface\n\u003cstrong\u003ePart I: Convex analysis\n\u003c\/strong\u003eConvex sets and their properties\nThe convex hull of a set. The interior of convex sets\nThe affine hull of sets. The relative interior of convex sets\nSeparation theorems for convex sets\nConvex functions\nClosedness, boundedness, continuity, and Lipschitz property of convex functions\nConjugate functions\nSupport functions\nDifferentiability of convex functions and the subdifferential\nConvex cones\nA little more about convex cones in infinite-dimensional spaces\nA problem of linear programming\nMore about convex sets and convex hulls\n\u003cstrong\u003ePart II: Set-valued analysis\u003c\/strong\u003e\nIntroduction to the theory of topological and metric spaces\nThe Hausdorff metric and the distance between sets\nSome fine properties of the Hausdorff metric\nSet-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps\nA base of topology of the spaceH\u003cem\u003ec\u003c\/em\u003e(\u003cem\u003eX\u003c\/em\u003e)\nMeasurable set-valued maps. Measurable selections and measurable choice theorems\nThe superposition set-valued operator\nThe Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations\nSpecial selections of set-valued maps\nDifferential inclusions\nFixed points and coincidences of maps in metric spaces\nStability of coincidence points and properties of covering maps\nTopological degree and fixed points of set-valued maps in Banach spaces\nExistence results for differential inclusions via the fixed point method\nNotation\nBibliography\nIndex \u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eAram Arutyunov\u003c\/strong\u003e, Moscow, Russia.\n\u003cstrong\u003eValerii Obukhovskii\u003c\/strong\u003e, Voronezh, Russia.\u003c\/p\u003e \u003cp\u003e\"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.\"\n\u003cem\u003eAdrian Petrusel in: Stud. Univ. Babes-Bolyai Math. 62(2017), No. 1, 137-138\u003c\/em\u003e \u003c\/p\u003e \u003cp\u003e\"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.\"\n\u003cem\u003eSeniorprof. Martin Weber, TU Dresden\u003c\/em\u003e \u003c\/p\u003e","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":48799982649579,"sku":"00000_00000_00000_00000","price":175.77,"currency_code":"SGD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0758\/4484\/5803\/files\/9783110460285-1.jpg?v=1781718714","url":"https:\/\/kinokuniya.com.sg\/zh\/products\/9783110460285","provider":"Books Kinokuniya Singapore","version":"1.0","type":"link"}