On the convergence, stability, data dependence results and the solution of a nonlinear integral equation by an efficient iterative scheme in Banach spaces

Temir, Seyit

doi:10.22075/ijnaa.2025.35661.5301

On the convergence, stability, data dependence results and the solution of a nonlinear integral equation by an efficient iterative scheme in Banach spaces

Articles in Press

Document Type : Research Paper

Author

Seyit Temir

Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040, Adıyaman, Türkiye

10.22075/ijnaa.2025.35661.5301

Abstract

In this paper, we study the convergence of an efficient fixed-point iterative scheme for contraction mappings. The iterative scheme converges strongly to the fixed point of contraction mappings in Banach spaces. Numerical examples are also provided to test the efficiency and effectiveness of the proposed iteration. We also prove that the iteration is the stability and data dependence. Finally, we apply the iteration scheme to find the solution of the nonlinear integral equation.

Keywords

Fixed point

data depence

iteration scheme

nonlinear integral equation

stability

contraction mappings

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