Fixed Point Results on Multi-Valued Generalized (α,β)-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.

Fixed point approximation for a class of generalized nonexpansive multi-valued mappings in Banach spaces

“…Fixed point theory for different types of single-valued and multi-valued mappings has attracted the attention of many researchers. Many types of iterative processes have been utilized to approximate the fixed points of multi-valued mappings in Banach spaces, (see, e.g., [1,2,6,8,16,17]). Let U be a Banach space with norm .…”