On some extensions of Banach's contraction principle and applications to the convergence and stability of some iterative processes

Abstract

In this paper, we obtain existence and uniqueness results of fixed points of nonlinear operators satisfying the condition of the form (Φ1,Φ2) given as a perturbation of Φ2 contraction by a convenable function Φ1 in metric and Banach spaces, which enable us to extend the Banach’s mapping principle and other results in the literature. Also, the Φ-quasi nonexpansive character of our context is shown in order to obtain results of convergence and stability of iterative processes of Mann and Ishikawa.