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.