IJPAM: Volume 18, No. 1 (2005)

THE EQUIVALENCE OF MANN AND ISHIKAWA
ITERATION METHODS WITH ERRORS FOR
LIPSCHITZIAN $\phi$-STRONGLY ACCRETIVE OPERATORS

Zeqing Liu$^1$, Li Wang$^2$, Soo Hak Shim$^3$, Shin Min Kang$^4$
$^1$Department of Mathematics
Liaoning Normal University
P.O. Box 200, Dalian, Liaoning, 116029, P.R. CHINA
e-mail: zeqingliu@dl.cn
$^2$Department of Science
Shenyang Institute of Aeronautical Engineering
P.O. Box 148, Shenyang, Liaoning, 110034, P.R. CHINA
$^{3,4}$Department of Mathematics
Research Institute of Natural Science
Gyeongsang National University
Chinju, 660-701, KOREA
$^4$e-mail: smkang@nongae.gsnu.ac.kr


Abstract.In this paper, we establish the equivalence between the convergences of Mann and Ishikawa Iteration methods with errors for Lipschitzian $\phi$-strongly accretive and $\phi$-strongly pseudocontractive operators, respectively, in Banach spaces. An example is also included to dwell upon the importance of the results obtained.

Received: September 12, 2004

AMS Subject Classification: 47H10, 47H15

Key Words and Phrases: Lipschitzian $\phi$-strongly accretive operator, $\phi$-Lipschitzian strongly pseudocontractive operator, Mann iteration sequence with errors, Ishikawa iteration sequence with errors

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 1