Convergence Theorems for -Strongly Accretive and -Hemicontractive Operators

Suppose that X is an arbitrary real Banach space and T: X X is a continuous -strongly accretive operator. It is shown that the nonlinear equation Tx f has a unique solution and under certain conditions both the Mann and Ishikawa iteration methods with errors introduced by Y. Xu Ž1998, J. Math. Anal. Appl. 224, 91 101. converge strongly to the solution. A related result deals with the approximation of fixed points of -hemicontractive operators