NEW GENERALIZATION OF THE BEST PROXIMITY POINT PROBLEM

Let (C, D) be a nonempty pair of disjoint subsets of a metric space. Main purpose of this paper is to present a range of a convergence sequence to u ∈ C ∪ D such that d(T u, fu) = dist(C, D), for mappings T, f : C ∪ D → C ∪ D. In fact, we give a generalization of best proximity point results for cyclic contractive mappings. To this end, we consider an example is presented to support the main result.