Fixed Point Results on Multi-Valued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in Banach Spaces

Abstract

In this paper, we provide and study the concept of multi-valued generalized (α,β)-nonexpansive mappings, which is the multi-valued version of the recently developed generalized (α,β)-nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings.

Keywords

• multi-valued generalized (<i>α</i>,<i>β</i>)-nonexpansive mappings
• M-iteration process
• uniformly convex Banach space
• fixed point
• strong convergence
• weak convergence