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

Abstract

Abstract In this paper, we propose a new iteration process, called multi-valued F-iteration process, for the approximation of fixed points. We introduce a new class of multi-valued generalized nonexpansive mappings satisfying a $$B_{\gamma ,\mu }$$ B γ , μ property. Moreover, we establish certain weak and strong convergence theorems in uniformly convex Banach spaces. We also discuss the stability of the modified F-iteration process. Furthermore, a numerical example is presented to illustrate the superiority of our results.