Convergence, stability and data dependence results for contraction and nonexpansive mappings by a new four step algorithm

Here we show that the UI-iteration scheme (Udofia and Igbokwe, [24]) can be used to approximate the fixed points of contraction and nonexpansive mappings. we prove a strong and weak convergence of the iteration scheme to the fixed point of contraction and nonexpansive mappings. We also prove that the scheme is Γ-stable and data dependent. Analytically and with numerical example we show that the UI-iteration scheme has a faster rate of convergence for contraction and nonexpansive mappings than some well known existing iteration schemes in literature. Finally, we apply the UI-iteration scheme to find the solution of constrained convex minimization problem.