Approximating Fixed Points of Bregman Generalized <i>α</i>-Nonexpansive Mappings

Abstract

In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern’s algorithm.

Keywords

• fixed point
• Bregman distance
• Bregman function
• Bregman–Opial property
• generalized α-nonexpansive mapping