Ishikawa and Mann iteration methods with errors for nonlinear equations of the accretive type

[摘要] Let E be an arbitrary Banach space and T: E --> E a Lipschitz strongly accretive operator. It is proved that for a given f is an element of E, 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 Tx = f. Furthermore, if E is a uniformly smooth Banach space and T: E --> E 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 Tx = f. Related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators, and the solution of the equation x + Tx = f, f is an element of E when T: E --> E is m-accretive. (C) 1997 Academic Press.

[发布日期] 1997-09-01