Stability of the Mann and Ishikawa Iteration Procedures for φ-Strong Pseudocontractions and Nonlinear Equations of the φ-Strongly Accretive Type

Abstract

We study the stability of the Mann and Ishikawa iteration procedures for the class of Lipschitz φ-strongly pseudocontractive maps in arbitrary real Banach spaces. As a consequence we study the stability of these iteration procedures for the iterative approximation of solutions of nonlinear equations of the φ-strongly accretive type. Furthermore, we prove that theT-stability of the Mann iteration procedure leads to the strong convergence (to the fixed point ofT) of the so-called Mann iteration method with errors introduced by Liu [J. Math. Anal. Appl.194(1995), 114–125].