A solution of a nonlinear Volterra integral equation with delay via a faster iteration method-Reference-Cited by-同舟云学术

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

Published:2023 Issue:1 Volume:8 Page:102-124
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Okeke Godwin Amechi¹²,Ofem Austine Efut³⁴,Abdeljawad Thabet⁵⁶,Alqudah Manar A.⁷,Khan Aziz⁵

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference41 articles.

1. M. Abbas, T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik, 66 (2014), 223–234.

2. R. P. Agarwal, D. O'Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal., 8 (2007), 61–79.

3. F. Ali, J. Ali, Convergence, stability, and data dependence of a new iterative algorithm with an application, Comput. Appl. Math., 39 (2020), 1–15. https://doi.org/10.1007/s40314-020-01316-2

4. F. Akutsah, O. K. Narain, K. Afassinou, A. A. Mebawondu, An iterative scheme for fixed point problems, Adv. Math. Sci. J., 10 (2021), 2295–2316. https://doi.org/10.37418/amsj.10.5.2

5. Y. Atalan, V. Karakaya, Iterative solution of functional Volterra-Fredholm integral equation with deviating argument, J. Nonlinear Convex Anal., 18 (2017), 675–684.

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