Convergence analysis for a new two-step iteration process for G-nonexpansive mappings with directed graphs

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In this paper, we introduce and study convergence analysis of a new two-step iteration process when applied to class of G-nonexpansive mappings. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space with a directed graph. Moreover, weak convergence theorem without making use of the Opial’s condition is proved. We also show the numerical experiment for supporting our main results and comparing rate of convergence of the proposed method with the Ishikawa iteration and the modified S-iteration.