Error Bounds for Approximation Solutions to Nonlinear Equations of Strongly Accretive Operators in Uniformly Smooth Banach Spaces

✍ Scribed by Lu-Chuan Zeng

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 175 KB
• Volume: 209
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5229

✦ Synopsis

Let X be a uniformly smooth Banach space and T : X ª X a strongly accretive operator. In this paper, we give the error bounds for the approximation solutions of the nonlinear equation Tx s f generated by both the Mann and the Ishikawa iteration process. On the other hand, let K be a nonempty convex subset of X and T : K ª K a strictly pseudocontractive mapping. The related results deal with the error bounds for the iterative approximation of the fixed point of T generated by these two processes.