Convergence of the S-iteration process for the multi-valued generalized ( \alpha -\beta )-nonexpansive mappings in Banach spaces

In this work, we first introduce the modified S-iteration method to approximate common fixed points of three multi-valued generalized ( \alpha -\beta )-nonexpansive mappings in the setting of Banach spaces. Then we prove some convergence theorems for these mappings by using it. Also, a numerical example is given to illustrate the main results. Furthermore, we introduce a one-step iterative process for generalized ( \alpha -\beta )-nonexpansive mappings and we prove strong convergence results for the one-step iterative process involving such mappings. Thus our results extend and generalise corresponding results in the contemporary literature.

Keywords:

Fixed point , multi-valued generalized (α-β)-nonexpansive mappings , uniformly convex Banach space