Asplund sets, differentiability and subdifferentiability of functions in Banach spaces

[摘要] We show that Asplund sets are effective tools to study differentiability of Lipschitz functions, and epsilon-subdifferentiability of lower semicontinuous functions on general Banach spaces. If a locally Lipschitz function defined on an Asplund generated space X = (TY) over bar has a minimal Clarke subdifferential mapping, then it is TBy-uniformly strictly differentiable on a dense G(delta) subset of X. Examples are given of locally Lipschitz functions that are TBy-uniformly strictly differentiable everywhere, but nowhere Frechet differentiable. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-11-15

[关键词] Asplund set;Asplund generated space;TB gamma-uniformly strict differentiability;M-differentiability and subdifferentiability