Minimax theorems for set-valued maps without continuity assumptions. (3rd May 2016)

• Record Type: Journal Article
• Authors: Patriche, Monica
• Is Part Of: Optimization. Volume 65:Number 5(2016)
• Page Start: 957
• Page End: 976
• Publication Date: 2016-05-03
• Subjects: minimax theorems -- fixed point theorem -- weakly naturally quasiconcave set-valued map -- S-transfer -convex set-valued map -- transfer properly S-quasiconvex -- weakly z-convex set-valued map; 49J35 -- 90C47; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1091822
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We introduce several classes of set-valued maps with new generalized convexity properties. We also obtain minimax theorems for set-valued maps which satisfy these convexity assumptions and which are not continuous. Our method consists of the use of a fixed point theorem for weakly naturally quasiconcave set-valued maps, defined on a simplex in a topological vector space, or of a constant selection of quasiconvex set-valued maps.