Upper-Semi Continuity With Respect to Non Weakly Compactly Generated Index and Asplund Spaces.

In this paper, using the upper semi-continuity of set-valued mapping with respect to non weakly compactly generated index and the sub-differential theory, the authors establish some results about separability, and the generic Fréchet differentiability of continuous convex functions. A characterization and some sufficient conditions for a Banach space to be an Asplund space is also established. [ABSTRACT FROM AUTHOR]