Fixed point iterations for Prešić-Kannan nonexpansive mappings in product convex metric spaces

Abstract

We introduce Prešić-Kannan nonexpansive mappings on the product spaces and show that they have a unique fixed point in uniformly convex metric spaces. Moreover, we approximate this fixed point by Mann iterations. Our results are new in the literature and are valid in Hilbert spaces, CAT(0) spaces and Banach spaces simultaneously.

Keywords

• convex metric space
• prešić kannan nonexpansive mapping
• fixed point
• mann iterative algorithm
• convergence
• primary 47h09, 47h10
• secondary 49m05