IJPAM: Volume 39, No. 3 (2007)

ON ITERATIVE SOLUTIONS OF NONLINEAR EQUATIONS
OF THE $\phi$-STRONGLY ACCRETIVE TYPE IN
UNIFORMLY SMOOTH BANACH SPACES

Shin Min Kang$^1$, Zeqing Liu$^2$, Chahn Yong Jung$^3$
$^1$Department of Mathematics
Research Institute of Natural Science
Gyeongsang National University
Jinju, 660-701, KOREA
e-mail: smkang@nongae.gsnu.ac.kr
$^2$Department of Mathematics
Liaoning Normal University
P.O. Box 200, Dalian, Liaoning, 116029, P.R. CHINA
e-mail: zeqingliu@sina.com.cn
$^3$Department of Business Administration
Gyeongsang National University
Jinju, 660-701, KOREA
e-mail: bb5734@nongae.gsnu.ac.kr


Abstract.Let $X$ be a real uniformly smooth Banach space and $T:X\to X$ be a demicontinuous $\phi$-strongly accretive operator. It is proved that the Ishikawa iteration method with errors converges strongly to the solutions of the equations $f=Tx$ and $f=x+Tx$, respectively. A related result deals with the iterative approximation of fixed points of $\phi$-hemicontractive operators. Our results extend some known results in the literature.

Received: July 19, 2007

AMS Subject Classification: 47H17, 47H15, 47H05

Key Words and Phrases: Ishikawa iteration sequence with errors, demicontinuous operator, $\phi$-strongly accretive operator, $\phi$-hemicontractive operator, uniformly smooth Banach space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 3