Iterative approximation of fixed points of generalized $ \alpha _{m} $-nonexpansive mappings in modular spaces

Abstract

Our aim of this work is to approximate the fixed points of generalized $ \alpha _{m} $-nonexpansive mappings employing $ AA $-iterative scheme in the structure of modular spaces. The results of fixed points for generalized $ \alpha _{m} $-nonexpansive mappings is proven in this context. Moreover, the stability of the scheme and data dependence results are given for $ m $-contraction mappings. In order to demonstrate that the $ AA $-iterative scheme converges faster than some other schemes for generalized $ \alpha_{m} $-nonexpansive mappings, numerical examples are shown at the end.

Keywords

• fixed point
• $ aa $-iteration
• modular space
• generalized $ \alpha_{m} $-nonexpansive mapping