A large averaging modified implicit iterative scheme with errors for finite family of asymtotically φ-demicontractive mappings

Document Type : Original Article


1 Department of Mathematics, University of Uyo, Uyo, Nigeria

2 Department of Mathematics, Michael Okpara University of Agriculture, University of Agriculture, Umidke, Nigeria


In this paper, a three-step implicit iteration process with errors is introduced  and  we prove strong convergence theorem of the new iterative scheme with some mild conditions on the real sequences to a common fixed point of finite family of asymptotically φ-demicontractive mappings defined on a closed convex subset of a Banach space. The new iterative scheme includes several well known explicit and implicit iterative schemes. The results in this paper generalize several strong convergence results in the literature.