Attainment and (sub)differentiability of the supremal convolution of a function and square of the norm

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• 作者：R. Cibulka^a ; ^{cibi@kma.zcu.cz} ; M. Fabian^b ; ^{fabian@math.cas.cz}
• 关键词：Supremal convolution ; Strong attainment ; Dense G未 set ; Subdifferential ; Farthest distance function ; Densely remotal set ; Fré ; chet and Gateaux differentiability ; Locally uniformly rotund norm
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：15 September, 2012
• 卷：393
• 期：2
• 页码：632-643
• 文件大小：296 K

摘要

Let be a Banach space whose norm is LUR. Under some mild assumptions, it is shown that the supremal convolution of a fairly general function on and the square of the norm is generically strongly attained. This contains a recent result of Bandyopadhyay and Dutta on farthest distance functions.