Strong Convergence Theorems for Asymptotically Weak G -Pseudo- Ψ -Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces

Abstract

A new concept of the asymptotically weak $G$-pseudo-$\mathrm{\Psi }$-contractive non-self-mapping $T:G\mapsto B$ is introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly and smooth Banach space. The proof methods are also different from some past common methods.