Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 22, No 1, (1996), 29p-32p
Abstract:
Let X be a Banach space equipped with norm || · ||. We say that || · || is Gâteaux
differentiable at x if for every h ∈ SX(|| · ||),
(∗) lim t→0 (||x + th|| − ||x||) / t exists.
We say that the norm || · || is Gâteaux differentiable if || · || is Gâteaux differentiable
at all x ∈ SX(|| · ||).
