An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application

Maryam Gharamah Alshehri, Faizan Ahmad Khan and Faeem Ali
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Maryam Gharamah Alshehri: Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Faizan Ahmad Khan: Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Faeem Ali: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India

Mathematics, 2022, vol. 10, issue 7, 1-16

Abstract: In this article, we study the JF iterative algorithm to approximate the fixed points of a non-linear operator that satisfies condition (E) in uniformly convex Banach spaces. Further, some weak and strong convergence results are presented for the same operator using the JF iterative algorithm. We also demonstrate that the JF iterative algorithm is weakly w 2 G -stable with respect to almost contractions. In connection with our results, we provide some illustrative numerical examples to show that the JF iterative algorithm converges faster than some well-known iterative algorithms. Finally, we apply the JF iterative algorithm to estimate the solution of a functional non-linear integral equation. The results of the present manuscript generalize and extend the results in existing literature and will draw the attention of researchers.

Keywords: iterative algorithms; non-linear operator (E); almost contraction; fixed points; Banach space; non-linear integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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