On convex functions having points of Gateaux differentiability which are not points of Fréchet differentiability

We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we provide related characterizations of infinite dimensional Banach spaces and of Banach spaces containing ł₁. Explicit examples are given. Some renormings of WCG Asplund spaces are made in this vein