We generalize a theorem of Ky Fan about the nearest distance between a closed convex set D in a Banach space E and its image by a function f:D→E,in several directions:(1)for noncompact sets D.when f(D)precompact:(2)f...We generalize a theorem of Ky Fan about the nearest distance between a closed convex set D in a Banach space E and its image by a function f:D→E,in several directions:(1)for noncompact sets D.when f(D)precompact:(2)for compact D and upper semicontinuous multifunction f:and more generally,(3)for noncompact D and upper semicontinuous multifunction f with f(D)Hausdorff precompact. In particular,we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions. whose values are convex closed bounded,thus not necessarily compact.展开更多
基金partially supported by the project"Geometrical functional analysis in Banach spaces:variational principles and global approximation"between Italy and Bulgaria
文摘We generalize a theorem of Ky Fan about the nearest distance between a closed convex set D in a Banach space E and its image by a function f:D→E,in several directions:(1)for noncompact sets D.when f(D)precompact:(2)for compact D and upper semicontinuous multifunction f:and more generally,(3)for noncompact D and upper semicontinuous multifunction f with f(D)Hausdorff precompact. In particular,we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions. whose values are convex closed bounded,thus not necessarily compact.
