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Convergence Theorems for φ-Strongly Accretive and φ-Hemicontractive Operators

✍ Scribed by Zeqing Liu; Shin Min Kang

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 104 KB
Volume: 253
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6973

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✦ Synopsis

Suppose that X is an arbitrary real Banach space and T : X ª X is a continuous -strongly accretive operator. It is shown that the nonlinear equation Tx s f has a unique solution and under certain conditions both the Mann and Ishikawa itera-Ž tion methods with errors introduced by Y. Xu 1998, J. Math. Anal. Appl. 224, . 91᎐101 converge strongly to the solution. A related result deals with the approximation of fixed points of -hemicontractive operators.

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