On Best Proximity Point Theorems and Fixed Point Theorems for p -Cyclic Hybrid Self-Mappings in Banach Spaces

Abstract

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent $(K,\lambda )$-hybrid $p$-cyclic self-mappings relative to a Bregman distance $D_f$, associated with a Gâteaux differentiable proper strictly convex function $f$ in a smooth Banach space, where the real functions $\lambda$ and $K$ quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping. Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.