Multivalued SK-contractions with respect to b-generalized pseudodistances

A new class of multivalued non-self-mappings, called SK-contractions with respect to b-generalized pseudodistances, is introduced and used to investigate the existence of best proximity points by using an appropriate geometric property. Some new fixed point results in b-metric spaces are also obtained. Examples are given to support the usability of our main result

Best proximity point theorems for α-nonexpansive mappings in Banach spaces

In this paper, we discuss sufficient and necessary conditions for the existence of best proximity points for non-self-a-nonexpansive mappings in Banach spaces. We obtain convergence results under some assumptions, and we prove the existence of common best proximity points for a family of non-self-a-nonexpansive mappings