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Ural Mathematical Journal, 2021, Volume 7, Issue 2, Pages 59–85
DOI: https://doi.org/10.15826/umj.2021.2.005
(Mi umj150)
 

This article is cited in 15 scientific papers (total in 15 papers)

A robust iterative approach for solving nonlinear Volterra delay integro-differential equations

Austine Efut Ofema, Unwana Effiong Udofiab, Donatus Ikechi Igbokwec

a Department of Mathematics, University of Uyo
b Department of Mathematics and Statistics, Akwa Ibom State University
c Department of Mathematics, Michael Okpara University of Agriculture
References:
Abstract: This paper presents a new iterative algorithm for approximating the fixed points of multivalued generalized $\alpha$-nonexpansive mappings. We study the stability result of our new iterative algorithm for a larger concept of stability known as weak $w^2$–stability. Weak and strong convergence results of the proposed iterative algorithm are also established. Furthermore, we show numerically that our new iterative algorithm outperforms several known iterative algorithms for multivalued generalized $\alpha$-nonexpansive mappings. Again, as an application, we use our proposed iterative algorithm to find the solution of nonlinear Volterra delay integro-differential equations. Finally, we provide an illustrative example to validate the mild conditions used in the result of the application part of this study. Our results improve, generalize and unify several results in the existing literature.
Keywords: Banach space, uniformly convex Banach space, multivalued generalized $\alpha$-nonexpansive mapping, convergence, nonlinear Volterra delay integro-differential equations.
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Document Type: Article
Language: English
Citation: Austine Efut Ofem, Unwana Effiong Udofia, Donatus Ikechi Igbokwe, “A robust iterative approach for solving nonlinear Volterra delay integro-differential equations”, Ural Math. J., 7:2 (2021), 59–85
Citation in format AMSBIB
\Bibitem{OfeUdoIgb21}
\by Austine~Efut~Ofem, Unwana~Effiong~Udofia, Donatus~Ikechi~Igbokwe
\paper A robust iterative approach for solving nonlinear Volterra delay integro-differential equations
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 2
\pages 59--85
\mathnet{http://mi.mathnet.ru/umj150}
\crossref{https://doi.org/10.15826/umj.2021.2.005}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4358914}
\elib{https://elibrary.ru/item.asp?id=47556642}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124264483}
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  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Ural Mathematical Journal
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