Title: The extension of continuity and generalized results for set-valued maps in convex analysis
Abstract: Abstract The paper is organized into two parts. In the first part, we establish some new vectorial set-valued variant of Hahn–Banach theorems with a K -concave continuous (resp. lower semicontinuous, upper semicontinuous) set-valued map dominated by a K -convex set valued map. The existence of the extension of continuity for dominated set-valued maps in order-complete topological vector spaces is also given. The main purpose of the second part is to present some applications to the existence theorems of K -quasigradients of K -convex set-valued maps, a generalized Lagrange multiplier theorem and a generalized sandwich theorem.
Publication Year: 2009
Publication Date: 2009-02-05
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 3
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