A new iterative approximation scheme for Reich–Suzuki-type nonexpansive operators with an application

• Published in: Journal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 26
• Main Authors: Ofem, Austine Efut, Işık, Hüseyin, Ali, Faeem, Ahmad, Junaid
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 02.03.2022; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Approximation; Banach space; Banach spaces; Contractive-like mapping; Convergence; Fixed points (mathematics); Game theory; Integral equations; Iterative methods; Iterative scheme; Mathematics; Mathematics and Statistics; Nonlinear integral equation; Stability; w 2 $w^{2}$ -stability; Iterative scheme; Nonlinear integral equation; 47H09; Contractive-like mapping; Banach space; 47H05; stability; 39B82

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 contra...