Best approximation, coincidence and fixed point theorems for quasi-lower semicontinuous set-valued maps in hyperconvex metric spaces

Suppose X is a compact admissible subset of a hyperconvex metric spaces M. and suppose F : X - M is a quasi-lower semicontinuous set-valued map whose values are nonempty admissible. Suppose also G : X - X is a continuous, onto quasi-convex set-valued map with compact, admissible values. Then there exists an X-0 is an element of X such that d(G(x(0)), F(x(0))) = inf(x is an element of X) d(x, F(x(0))). As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results, generalize some well-known results in literature. (C) 2009 Elsevier Ltd. All rights reserved.