Ishikawa and Mann Iteration Methods with Errors for Nonlinear Equations of the Accretive Type*

Let E be an arbitrary Banach space and T: EªE a Lipschitz strongly accretive operator. It is proved that for a given fgE, the Ishikawa and the Mann iteration methods with errors introduced by L.-S. Liu J. Math. Anal. Appl. 194, 1995, 114]125. converge strongly to the solution of the equation Txsf. Furthermore, if E is a uniformly smooth Banach space and T: EªE is demicontinuous and strongly accretive, it is also proved that both the Ishikawa and the Mann iteration methods with errors converge strongly to the solution of the equation Txsf. Related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators, and the solution of the equation xqTxsf, fgE when T: EªE is m-accretive.