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Construction of Zeros of Accretive Mappings

โœ Scribed by A. Udomene


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
86 KB
Volume
262
Category
Article
ISSN
0022-247X

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โœฆ Synopsis


Let E be a real uniformly smooth Banach space. Implicit iterative methods for the approximation of zeros of m-accretive mappings A: E ยช 2 E are constructed and an application to the construction of an explicit iterative method is given. Our Banach space need not admit duality maps which are weakly sequentially continuous at zero. In particular our theorems apply to L spaces 1p -ฯฑ. แฎŠ 2001 p


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Let X be a real Banach space and T : D(T) C X --\\* 2 X be an m-accretive operator. Let C : D(T) C X --~ X be a bounded operator (not necessarily continuous) such that C(T -+-i)-1 is compact. Suppose that for every x โ€ข D(T) with Hxll > r, there exists jx 6 Jx such that > o, (,) for all u E Tx. Then