Yuguang Xu, Fang Xie
Stability of Mann Iterative Process with Random Errors for the Fixed Point of Strongly-Pseudocontractive Mapping in Arbitrary Banach Spaces
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 58, 93-100(2004)
47H15 Equations involving nonlinear operators, See also {58E07 for abstract bifurcation theory}
47H17 Methods for solving equations involving nonlinear operators, See also {58C15}, {For numerical analysis, See 65J15}
Abstract: Suppose that $X$ is a arbitrary real Banach space
and $T:X\rightarrow X$ is a Strongly pseudocontractive mapping.
It is proved that certain Mann iterative process
with random errors for the fixed point of $T$ is
stable(almost stable) with respect to $T$
with(without) Lipschitz condition.
And, two related results are obtained
that deals with stability(or almost stability) of Mann iterative process
for solution of nonlinear equations
with strongly accretive mapping.
Consequently, the corresponding results of
Osilike are improved.

Keywords: strongly pseudocontractive mapping, strongly accretive mapping, Mann iterative process with random errors, stable, almost stable
Notes: This work is supported by the foundation of Yunnan Sci. Tech. Commission, China(2002A0058m)