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APPROXIMATION OF FIXED POINTS AND THE SOLUTION OF A NONLINEAR INTEGRAL EQUATION
Faeem Ali,Javid Ali,Rosana Rodr´ıguez-L´opez 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.5
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.