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Research Article | Open Access

On fixed-point approximations for a class of nonlinear mappings based on the JK iterative scheme with application

Junaid Ahmad1( ), Kifayat Ullah2, Hasanen A. Hammad3,4, Reny George5( )
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan
Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
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Abstract

The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type.

Keywords

iteration schemeconvergence resultsfixed point techniquenonexpansive mappinguniformly convex Banach space
CLC number: 47H09, 47H10

References

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13663-13679
DOI: 10.3934/math.2023694

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Cite this article:
Ahmad J, Ullah K, Hammad HA, et al. On fixed-point approximations for a class of nonlinear mappings based on the JK iterative scheme with application. AIMS Mathematics, 2023, 8(6): 13663-13679. https://doi.org/10.3934/math.2023694

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Received: 26 February 2023
Revised: 13 March 2023
Accepted: 20 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)