Proximal quasi-normal structure in convex metric spaces

Abstract

We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasi-normal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. Convex Anal. 14 (2013), 653-659].

Keywords

• best proximity point
• proximal quasi-normal structure
• relatively kannan nonexpansive mapping
• convex metric space
• 47h10
• 47h09
• 46b20