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http://dx.doi.org/10.22771/nfaa.2021.26.05.01

APPROXIMATION OF FIXED POINTS AND THE SOLUTION OF A NONLINEAR INTEGRAL EQUATION  

Ali, Faeem (Department of Mathematics, Aligarh Muslim University)
Ali, Javid (Department of Mathematics, Aligarh Muslim University)
Rodriguez-Lopez, Rosana (Department of Statistics, Mathematical Analysis and Optimization Faculty of Mathematics, University of Santiago de Compostela)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.5, 2021 , pp. 869-885 More about this Journal
Abstract
In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.
Keywords
Iteration processes; Zamfirescu operator; fixed point; mixed Volterra-Fredholm functional nonlinear integral equation;
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