Convergence results for Zamfirescu operators and \((\alpha, \beta)\) nonexpansive type 1 mapping with applications

Abstract

In this paper, we introduce a new iterative scheme for approximating fixed points of Zamfirescu operators and generalized \((\alpha, \beta)\)-nonexpansive type-1 mappings in uniformly convex Banach spaces. We establish strong and weak convergence results under suitable conditions. Furthermore, we prove stability and compare the rate of convergence with several existing iterative methods, showing that the proposed scheme converges faster. Numerical examples and an application to a nonlinear integral equation arising in infectious disease modeling are provided to support the theoretical results.