Abstract
In this paper we first review the theory of weak differentiability with some improvements and unifications of existing results; then we introduce an extended variant of this notion and establish its basic properties; finally we use the weak differentiability and its variant to develop new calculus results in variational analysis for the theory of generalized differentiation and the sequential normal compactness. In this way we demonstrate that the weak differentiability and its variant, in contrast to the usual differentiability, are in fact more suitable for Frechet and limiting/Mordukhovich constructions in variational analysis.
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