ON M-ITERATIVE SCHEME FOR MAPPINGS WITH ENRICHED (C) CONDITION IN BANACH SPACES

In this paper, we approximate fixed points of mappings satisfying enriched (C) condition under a modified three-step M-iterativescheme in a Banach space setting. First, we establish a weak convergence theorem and then obtain several strong convergence theorems for our iterative scheme under some mild conditions. A numerical example of mappings satisfying enriched (C) condition is used that does not satisfy the ordinary (C) condition to support our main outcome. Numerical computations and graphs obtained from different iterative schemes show that the studied scheme provides a better rate of convergence as compared to some other schemes of the literature. As an application of our main result, we provide a projection type iterative scheme for solving split feasibility problems (SFP) on a Hilbert space setting.