Zeqing Liu, Jeong Sheok Ume, Shin Min Kang
Strong Convergence and pseudo Stability for Operators of the $\phi$-accretive type in uniformly smooth Banach Spaces
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 59, 29-40(2005)

MSC:

47H05 Monotone operators (with respect to duality)

47H06 Accretive operators, dissipative operators, etc.

47H10 Fixed-point theorems, See also {54H25, 55M20, 58C30}

Abstract: Let $X$ be a uniformly Banach space
and let $T:X \to X$ be a $\phi$-strongly quasi-accretive
operator.
It is proved that, under suitable conditions,
the Ishikawa iterative process with errors both converges strongly
to the unique zero of $T$ and is pseudo stable. A few related
results deal with the convergence and stability of the
Ishikawa iterative process with errors to the solutions
of the equations $Tx =f$ and $x+Tx =f$, respectively,
when $T:X \to X$ is $\phi$-strongly accretive.
Our results extend, improve, and unify the results
due to Chidume \cite{ume2}, \cite{ume3} and Zhou \cite{ume18}.

Keywords: Ishikawa iterative process with errors, $\phi$-strongly quasi-accretive operator, $\phi$-strongly accretive operator, stability, uniformly smooth Banach space.
Notes: This research was financially supported by Changwon National
University in 2004