%0 Journal Article %T Convergence Theorems for Monotone Generalized α-Nonexpansive Mappings in Ordered Banach Space by a New Four-Step Iteration Process with Application %J Communications in Nonlinear Analysis %I Research & Science Group Ltd. %Z 2371-7920 %A Udofia, Unwana %A Igbokwe, Donatus %D 2023 %\ 03/01/2023 %V 11 %N 1 %P 1-18 %! Convergence Theorems for Monotone Generalized α-Nonexpansive Mappings in Ordered Banach Space by a New Four-Step Iteration Process with Application %K monotone %K generalized α-Nonexpansive mapping %K Ordered Banach space %K fixed point %K contraction mapping %K Split Feasibility Problem %R %X 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 FeasibilityProblem (SFP). Our result complements, extends and generalizes some existing results in literature. %U https://www.cna-journal.com/article_138222_1738741236af6d9a5f4d9e1635ca3260.pdf