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

Authors

1 DEPARTMENT OF MATHEMATICS AND STATISTICS, AKWA IBOM STATE UNIVERSITY, IKOT AKPADEN, MKPAT ENIN, NIGERIA.

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

Abstract

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.

Keywords

Communications in Nonlinear Analysis
Volume 9, Issue 2
October 2021
Pages 1-17

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