A characterization of weak proximal normal structure and best proximity pairs

Abstract

The aim of this paper is to address an open problem given in [Kirk et al. in J Math Anal Appl 463:461–476, (2018)]. We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove the existence of a best proximity pair in the setting of reflexive Banach spaces.