A solution of a nonlinear Volterra integral equation with delay via a faster iteration method

Godwin Amechi Okeke; Austine Efut Ofem; Thabet Abdeljawad; Manar A. Alqudah; Aziz Khan; Godwin Amechi Okeke; Austine Efut Ofem; Thabet Abdeljawad; Manar A. Alqudah; Aziz Khan

doi:10.3934/math.2023005

AIMS Mathematics

2023, Volume 8, Issue 1: 102-124. doi: 10.3934/math.2023005

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Research article

A solution of a nonlinear Volterra integral equation with delay via a faster iteration method

1.
Department of Mathematics, College of Science and Technology, Covenant University, Canaanland, KM 10, Idiroko Road, Ota, Ogun State, Nigeria
2.
Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria
3.
Department of Mathematics, University of Uyo, Uyo, Nigeria
4.
Department of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
5.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematical Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 21 May 2022 Revised: 02 September 2022 Accepted: 15 September 2022 Published: 27 September 2022
MSC : 34B10, 34B15, 26A33

The purpose of this article is to study the convergence, stability and data dependence results of an iterative method for contractive-like mappings. The concept of stability considered in this study is known as $ w^2 $-stability, which is larger than the simple notion of stability considered by several prominent authors. Some illustrative examples on $ w^2 $-stability of the iterative method have been presented for different choices of parameters and initial guesses. As an application of our results, we establish the existence, uniqueness and approximation results for solutions of a nonlinear Volterra integral equation with delay. Finally, we provide an illustrative example to support the application of our results. The novel results of this article extend and generalize several well known results in existing literature.
- Banach space,
- data dependence,
- $ w^2 $-stability,
- contractive-like mapping,
- nonlinear Volterra integral equation,
- fixed point
Citation: Godwin Amechi Okeke, Austine Efut Ofem, Thabet Abdeljawad, Manar A. Alqudah, Aziz Khan. A solution of a nonlinear Volterra integral equation with delay via a faster iteration method[J]. AIMS Mathematics, 2023, 8(1): 102-124. doi: 10.3934/math.2023005

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Abstract

The purpose of this article is to study the convergence, stability and data dependence results of an iterative method for contractive-like mappings. The concept of stability considered in this study is known as $ w^2 $-stability, which is larger than the simple notion of stability considered by several prominent authors. Some illustrative examples on $ w^2 $-stability of the iterative method have been presented for different choices of parameters and initial guesses. As an application of our results, we establish the existence, uniqueness and approximation results for solutions of a nonlinear Volterra integral equation with delay. Finally, we provide an illustrative example to support the application of our results. The novel results of this article extend and generalize several well known results in existing literature.

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