IJPAM: Volume 71, No. 2 (2011)

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

Zeqing Liu$^1$, Li Wang$^2$, Young Chel Kwun$^3$, Shin Min Kang$^4$
$^1$Department of Mathematics
Liaoning Normal University
Dalian, Liaoning 116029, P.R. CHINA
$^2$Department of Science
Shenyang Aerospace University
Shenyang, Liaoning 110034, P.R. CHINA
$^3$Department of Mathematics
Dong-A University
Pusan 614-714, KOREA
e-mail: [email protected]
$^4$Department of Mathematics and RINS
Gyeongsang National University
Jinju 660-701, KOREA


Abstract. The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for uniformly continuous and $\phi$-strongly accretive or $\phi$-strongly pseudocontractive operators in Banach spaces are proved. Two examples which dwell upon the importance of our results are also included.

Received: June 17, 2011

AMS Subject Classification: 47H10, 47H15

Key Words and Phrases: uniformly continuous and $\phi$-strongly accretive operator, uniformly continuous and $\phi$-strongly pseudocontractive operator, Mann iteration method with errors, Ishikawa iteration method with errors

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 71
Issue: 2