Approximation theorems for G-nonexpansive mappings in convex metric spaces by three step iterations

Abstract

In this article, we study the convergence behavior of G-nonexpansive mappings for three-step iterations in convex metric space along with the directed graph. We demonstrate the Δ-convergence as well as the strong convergence results for these mappings. For supporting our main results we presented a numerical example and convergence comparison of modified Thianwan iteration with SP iteration scheme and Noor iteration scheme.

Keywords

• Δ-convergence as well as strong convergence
• Convex metric spaces
• Directed graph