{"product_id":"convex-and-set-valued-analysis-selected-topics-paperback","title":"Convex and Set-Valued Analysis: Selected Topics - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eAram V. Arutyunov\u003c\/b\u003e (Author), \u003cb\u003eValeri Obukhovskii\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\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: \u003cbr\u003e\u003c\/strong\u003ePreface\u003cbr\u003e\u003cstrong\u003ePart I: Convex analysis\u003cbr\u003e\u003c\/strong\u003eConvex sets and their properties\u003cbr\u003eThe convex hull of a set. The interior of convex sets\u003cbr\u003eThe affine hull of sets. The relative interior of convex sets\u003cbr\u003eSeparation theorems for convex sets\u003cbr\u003eConvex functions\u003cbr\u003eClosedness, boundedness, continuity, and Lipschitz property of convex functions\u003cbr\u003eConjugate functions\u003cbr\u003eSupport functions\u003cbr\u003eDifferentiability of convex functions and the subdifferential\u003cbr\u003eConvex cones\u003cbr\u003eA little more about convex cones in infinite-dimensional spaces\u003cbr\u003eA problem of linear programming\u003cbr\u003eMore about convex sets and convex hulls\u003cbr\u003e\u003cstrong\u003ePart II: Set-valued analysis\u003c\/strong\u003e\u003cbr\u003eIntroduction to the theory of topological and metric spaces\u003cbr\u003eThe Hausdorff metric and the distance between sets\u003cbr\u003eSome fine properties of the Hausdorff metric\u003cbr\u003eSet-valued maps. Upper semicontinuous and lower semicontinuous set-valued maps\u003cbr\u003eA base of topology of the spaceH\u003cem\u003ec\u003c\/em\u003e(\u003cem\u003eX\u003c\/em\u003e)\u003cbr\u003eMeasurable set-valued maps. Measurable selections and measurable choice theorems\u003cbr\u003eThe superposition set-valued operator\u003cbr\u003eThe Michael theorem and continuous selections. Lipschitz selections. Single-valued approximations\u003cbr\u003eSpecial selections of set-valued maps\u003cbr\u003eDifferential inclusions\u003cbr\u003eFixed points and coincidences of maps in metric spaces\u003cbr\u003eStability of coincidence points and properties of covering maps\u003cbr\u003eTopological degree and fixed points of set-valued maps in Banach spaces\u003cbr\u003eExistence results for differential inclusions via the fixed point method\u003cbr\u003eNotation\u003cbr\u003eBibliography\u003cbr\u003eIndex \u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAram Arutyunov\u003c\/strong\u003e, Moscow, Russia. \u003cbr\u003e\u003cstrong\u003eValerii Obukhovskii\u003c\/strong\u003e, Voronezh, Russia.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 209\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.5 x 9.4 x 6.6 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 30, 2016\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":48266214539513,"sku":"9783110460285","price":103.66,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/T-W-iBhqHs9783110460285.webp?v=1775671893","url":"https:\/\/bookscloud.io\/products\/convex-and-set-valued-analysis-selected-topics-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}