"I, P(GAP201/12/0436)" . . . "RIV/00216208:11320/14:10285323!RIV15-MSM-11320___" . . "pointwise Lipschitz mapping; sigma-directionally porous set; Hadamard directional derivatives; directional derivatives; Hadamard differentiability; Gateaux differentiability"@en . . . . "0944-6532" . . . . "Gateaux and Hadamard Differentiability via Directional Differentiability" . "21" . "Gateaux and Hadamard Differentiability via Directional Differentiability" . . "RIV/00216208:11320/14:10285323" . "Gateaux and Hadamard Differentiability via Directional Differentiability"@en . "11"^^ . "1"^^ . "000342730400006" . "Gateaux and Hadamard Differentiability via Directional Differentiability"@en . "[A65D7B9D8525]" . "Journal of Convex Analysis" . "1"^^ . "11320" . . "Zaj\u00ED\u010Dek, Lud\u011Bk" . "Let X be a separable Banach space, Y a Banach space and f : X -> Y an arbitrary mapping. Then the following implication holds at each point x is an element of X except a sigma-directionally porous set: If the one-sided Hadamard directional derivative f(H+)'(x,u) exists in all directions u from a set S-x subset of X whose linear span is dense in X, then f is Hadamard differentiable at x. This theorem improves and generalizes a recent result of A. D. Ioffe, in which the linear span of S-x equals X and Y = R. An analogous theorem, in which f is pointwise Lipschitz, and which deals with the usual one-sided derivatives and Gateaux differentiability is also proved. It generalizes a result of D. Preiss and the author, in which f is supposed to be Lipschitz." . "DE - Spolkov\u00E1 republika N\u011Bmecko" . . "Let X be a separable Banach space, Y a Banach space and f : X -> Y an arbitrary mapping. Then the following implication holds at each point x is an element of X except a sigma-directionally porous set: If the one-sided Hadamard directional derivative f(H+)'(x,u) exists in all directions u from a set S-x subset of X whose linear span is dense in X, then f is Hadamard differentiable at x. This theorem improves and generalizes a recent result of A. D. Ioffe, in which the linear span of S-x equals X and Y = R. An analogous theorem, in which f is pointwise Lipschitz, and which deals with the usual one-sided derivatives and Gateaux differentiability is also proved. It generalizes a result of D. Preiss and the author, in which f is supposed to be Lipschitz."@en . . . . . "17957" . . "3" . . .