Extension theorems for vector valued maps
نویسندگان
چکیده
منابع مشابه
Extension theorems for vector valued maps
We revisit studies on extension of Lipschitz maps and obtain new results about extension of displacements of bounded strain tensors. These questions are of interest in elasticity theory, optimal designs, as well as in functional analysis. Résumé Nous discutons l’extension d’applications Lipschitziennes et donnons, entre autres, une nouvelle démonstration d’un théorème de Schönbeck. Puis nous ét...
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This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2006
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2005.04.005