Approximating the solution of a nonlinear delay integral equation by an efficient iterative algorithm in hyperbolic spaces

Austine Efut Ofem; Hüseyin Işik; Godwin Chidi Ugwunnadi; Reny George; Ojen Kumar Narain; Austine Efut Ofem; Hüseyin Işik; Godwin Chidi Ugwunnadi; Reny George; Ojen Kumar Narain

doi:10.3934/math.2023762

AIMS Mathematics

2023, Volume 8, Issue 7: 14919-14950. doi: 10.3934/math.2023762

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Approximating the solution of a nonlinear delay integral equation by an efficient iterative algorithm in hyperbolic spaces

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2.
Department of Engineering Science, Bandırma Onyedi Eylül University, 10200 Bandırma, Balıkesir, Turkey
3.
Department of Mathematics, University of Eswatini, Kwaluseni, Eswatini
4.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa
5.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Received: 10 December 2022 Revised: 28 March 2023 Accepted: 29 March 2023 Published: 21 April 2023
MSC : 26A33, 34B10, 34B15

In this article, we propose the modified AH iteration process in Hyperbolic spaces to approximate the fixed points of mappings enriched with condition $ (E) $. The data dependence result of the proposed iteration process is studied for almost contraction mappings. Further, we obtain several new strong and $ \vartriangle $-convergence results of the proposed iteration algorithm for the class of mappings enriched with the condition $ (E) $. Also, we illustrate the efficiency of our results over existing results in literature with the aid of some numerical examples. Finally, we use our main results to find the solution of nonlinear integral equation with two delays.
Citation: Austine Efut Ofem, Hüseyin Işik, Godwin Chidi Ugwunnadi, Reny George, Ojen Kumar Narain. Approximating the solution of a nonlinear delay integral equation by an efficient iterative algorithm in hyperbolic spaces[J]. AIMS Mathematics, 2023, 8(7): 14919-14950. doi: 10.3934/math.2023762

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Abstract

In this article, we propose the modified AH iteration process in Hyperbolic spaces to approximate the fixed points of mappings enriched with condition $ (E) $. The data dependence result of the proposed iteration process is studied for almost contraction mappings. Further, we obtain several new strong and $ \vartriangle $-convergence results of the proposed iteration algorithm for the class of mappings enriched with the condition $ (E) $. Also, we illustrate the efficiency of our results over existing results in literature with the aid of some numerical examples. Finally, we use our main results to find the solution of nonlinear integral equation with two delays.

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