Please help me to investigate Gateaux and Frechet differentiability of the functional $x \rightarrow ||x||_c$ depending on $x \in c$. The same about functionals $x \rightarrow ||x||_{c_0},\ x \in c_0$ and $x \rightarrow ||x||_{L_1[0,1]},\ x \in L_1[0,1]$.
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