Yuguang Xu
Iterative Processes with Random Errors for Fixed Point of $\Phi$-Pseudocontractive Operator
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 59, 87-97(2005)
47H06 Accretive operators, dissipative operators, etc.
47H10 Fixed-point theorems, See also {54H25, 55M20, 58C30}
47H17 Methods for solving equations involving nonlinear operators, See also {58C15}, {For numerical analysis, See 65J15}
Abstract: The purpose of this paper is to introduce
$\Phi$-pseudo-contractive operators---a class of operators which
is much more general than the important class of strongly
pseudocontractive operators and $\phi$-strongly pseudocontractive
operators, and to study problems of approximating fixed points by
Ishikawa and Mann iterative processes with random errors for
$\Phi$-pseudocontractive operators. As applications, the iterative
approximative methods for the solution of equation with
$\Phi$-accretive operator are obtained. The results presented in
this paper improve, generalize and unify the corresponding results
of Chang \cite{xu3}-\cite{xu4}, Chidume \cite{xu5}-\cite{xu10},
Deng \cite{xu12}, Ding \cite{xu13}-\cite{xu14}, Liu \cite{xu16},
Osilike \cite{xu18}, Xu \cite{xu19}, Zhou \cite{xu20}.

Keywords: Duality mapping, Mann iteration sequence, Ishikawa iteration sequence, $\Phi$ -pseudocontractive operator.
Notes: This work is supported by the Foundation of Yunnan Sci. Tech.
Commission of P. R. China (No.2002A0058M)