The Method of Lines and the Approximation of Zeros of m-Accretive Operators in General Banach Spaces

✍ Scribed by A.G. Kartsatos; K.Y. Shin

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 533 KB
• Volume: 113
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1994.1117

✦ Synopsis

It is shown that a zero of an m-aceretive operator (T: D(T) \subset X \rightarrow 2^{x}), in a general Banach space (X), can be approximated via methods of lines for associated evolution equations. Results of Browder for (single-valued) locally defined continuous accretive operators (T) in spaces (X) with uniformly convex duals, or uniformly continuous accretive operators (T) in general Banach spaces (X), are extended to the present case. Results of Reich for (\mathrm{m})-accretive operators in reflexive Banach spaces are also extended to the present setting. Unlike Browder's results, our estimates do not use the modulus of continuity of the operators (T) or the duality mapping of (X). Kobayashi-type estimates are used for the bounds involving the normed differences between the endpoints of the methods of lines and a zero of (T). O 1994 Academic Press, Inc