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 ∈ X such that d ( G ( x 0 ) , F ( x 0 ) ) = inf x ∈ 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.