A new iterative approximation scheme for Reich–Suzuki-type nonexpansive operators with an application
Austine Efut Ofem, Hüseyin Işık, Faeem Ali, Junaid Ahmad
Abstract
Abstract In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The $w^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>w</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of $w^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>w</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.