Strong Convergence Theorems for Hybrid Mixed Type Nonlinear Mappings in Banach Spaces

Abstract

In this paper, we introduce a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some strong convergence theorems for mentioned scheme and mappings in Banach spaces. Our results extend and generalize the corresponding results recently announced by Wei and Guo [16] (Comm. Math. Res. 31(2015), 149-160) and many others.

Keywords

• asymptotically nonexpansive mapping
• non-self asymptotically nonexpansive mappings in the intermediate sense
• new two-step iteration scheme of hybrid mixed type
• common fixed point
• banach space
• strong convergence