Equivalent conditions for the generic Frechet differentiability of a given convex Lipschitz function f defined on a separable Banach space are established. The conditions are in terms of a majorization of f by a ;Approximation by smooth convex functions and questions on the Smooth Variational Principle for a continuous convex function defined on a WCG space are also studied.;A class of continuous convex functions defined on a Banach space (not necessarily an Asplund space) is defined. This class of functions is found to exhibit similar properties possessed by the norm of an Asplund space.;We also construct a uniformly smooth norm on a separable Banach space X that contains an isomorphic copy of ;An extension of norms from a closed subspace of a Banach space to the whole space that preserves various types of rotundity possessed by the subspace norms is constructed. We also construct a strictly convex norm such that a prescribed set of points lies on the unit sphere of this norm.
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