Convergence Theorems for Monotone Generalized α-Nonexpansive Mappings in Ordered Banach Space by a New Four-Step Iteration Process With Application

Document Type : Original Article


1 Department of Mathematics and Statistics, Akwa Ibom state University, Ikot Akpaden, Mkpatenin, Nigeria

2 Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.


We introduce a new four-step iterative algorithm and show that the new algorithm converges faster than a number of existing iterative algorithms for contraction mappings. We prove strong and weak convergence results for approximating fixed points of monotone generalized α-nonexpansive mappings. Further, we utilize our proposed algorithm to solve Split Feasibility Problem (SFP). Our result complements, extends and generalizes some existing results in literature.