Best Proximity Points of -Cyclic Contractions with Property UC

Abstract

We initiate the notion of generalized - cyclic contraction mappings with respect to an auxiliary function and investigate the existence of a best proximity point of such mappings in the setting of metric spaces. We also prove the uniqueness of a fixed point, when we assume an additional condition, named as: property UC. Moreover, we discuss the existence and uniqueness of a fixed point of -cyclic orbital contractions in the context of (b-metric) metric spaces.