A ROBUST ITERATIVE APPROACH FOR SOLVING NONLINEAR VOLTERRA DELAY INTEGRO–DIFFERENTIAL EQUATIONS

Austine Efut Ofem     (Department of Mathematics, University of Uyo, Uyo, Nigeria)
Unwana Effiong Udofia     (Department of Mathematics and Statistics, Akwa Ibom State University, Ikot Akpaden, Mkpatenin, Nigeria)
Donatus Ikechi Igbokwe     (Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria)

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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References


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DOI: http://dx.doi.org/10.15826/umj.2021.2.005

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