A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations

Hasanen A. Hammad (), Habib ur Rehman and Manuel De la Sen
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Hasanen A. Hammad: Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
Habib ur Rehman: Department of Mathematics, Monglkut’s University of Technology, Bangkok 10140, Thailand
Manuel De la Sen: Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Bizkaia, Spain

Mathematics, 2022, vol. 10, issue 22, 1-26

Abstract: This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive mappings (RSTN mappings, for short). Additionally, we demonstrate that for almost contraction mappings, the proposed algorithm converges faster than a variety of other current iterative schemes. Furthermore, the new iterative scheme’s ω 2 —stability result is established and a corroborating example is given to clarify the concept of ω 2 —stability. Moreover, weak as well as a number of strong convergence results are demonstrated for our new iterative approach for fixed points of RSTN mappings. Further, to demonstrate the effectiveness of our new iterative strategy, we also conduct a numerical experiment. Our major finding is applied to demonstrate that the two-dimensional (2D) Volterra integral equation has a solution. Additionally, a comprehensive example for validating the outcome of our application is provided. Our results expand and generalize a number of relevant results in the literature.

Keywords: RSTN mapping; almost contraction mapping; ? 2 —stability; fixed point methodology; nonlinear integral problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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