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Proximal analysis in reflexive smooth Banach spaces

✍ Scribed by M. Bounkhel; R. Al-Yusof

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 463 KB
Volume: 73
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.04.077

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✦ Synopsis

In the present paper, we introduce and study a new proximal normal cone in reflexive Banach spaces in terms of a generalized projection operator. Two new variants of generalized proximal subdifferentials are also introduced in reflexive smooth Banach spaces. The density theorem for both proximal subdifferentials has been proved in p-uniformly convex and q-uniformly smooth Banach spaces. Various important properties and applications of our concepts are also proved.

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