Fixed points of two types of non-cyclic contractions and their relationship with best proximity points of the corresponding cyclic contractions

Let and be nonempty subsets of metric space . In this paper, first we introduce two types of non-cyclic contractions on Then we study the existence and uniqueness of an optimal pair of fixed points for such mappings by considering property UC, in metric spaces. Our main results are generalization of recent best proximity points theorems for the corresponding cyclic contractions due to Di Bari-Suzuki-Vetro and Felicit-Eldred.