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

Suppose XX is a compact admissible subset of a hyperconvex metric spaces MM, and suppose F:X⊸MF:X⊸M is a quasi-lower semicontinuous set-valued map whose values are nonempty admissible. Suppose also G:X⊸XG:X⊸X is a continuous, onto quasi-convex set-valued map with compact, admissible values. Then there exists an x0∈Xx0∈X such that d(G(x0),F(x0))=infx∈Xd(x,F(x0)). 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.