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

We study the stability of the Mann and Ishikawa iteration procedures for the class of Lipschitz f-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 f-strongly accretive type. Furthermore, we prove that the T-stability of the Mann iteration procedure leads to the strong convergence to the fixed point of T.of the so-called Mann iteration method with errors introduced by Liu w J. Math. Anal. Appl. 194 1995., 114]125x.