Let be a measurable space, a Banach space whose characteristic of noncompact convexity is less than 1, a bounded closed convex subset of , the family of all compact convex subsets of We prove that a set-valued nonexpansive mapping has a fixed point. Furthermore, if is separable then we also prove that a set-valued nonexpansive operator has a random fixed point.
In this note we derive a theorem about the common fixed point set of commuting nonexpansive mappings defined in Cartesian products of separable spaces. The proof is based on a method due to R. E. Bruck.
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...
We introduce the relative fixed point index for a class of noncompact operators on special subsets of non locally convex spaces.
We consider a Banach space, which comes naturally from and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings defined on weakly compact, convex sets.