Korean J. Math. Vol. 31 No. 3 (2023) pp.269-294
DOI: https://doi.org/10.11568/kjm.2023.31.3.269

Approximation results of a three step iteration method in Banach Space

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Published: Sep 30, 2023
Keywords:
nonexpansive mapping, stability, Uniformly Convex Banach Space, Contractive like mapping, Weak Convergence, Strong Convergence
Mathematics Subject Classification:
47H09, 47H10

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Omprakash Sahu
Department of Mathematics, Babu Pandhri Rao Kridatt Govt. College Silouti, Dhamtari(C.G.) 493770, India
Amitabh Banerjee
Department of Mathematics, Govt. J. Y. Chhattisgarh College, Raipur, Raipur(C.G.) 492001, India

Abstract

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.



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