Convergence and Stability of the Ishikawa Iterative Process for a class of ϕ-quasinonexpansive Mappings

Abstract

The paper analyzes the convergence of Ishikawa iteration to the fixed point of a class of '-quasinonexpansive mappings in uniformly convex Banach spaces, as well as the stability of the Ishikawa iteration used in approximating the fixed point. The work not only confirmed Ishikawa iteration’s convergence and stability to the fixed point of '-quasinonexpansive mappings, but it also pointed the way for future research in the estimate of fixed points of ϕ-quasinonexpansive mappings.

Keywords

• ishikawa iterative process, φ-quasinonexpansive mappings, uniformly convex banach space, stability of the iteration