An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions

S. Rolewicz

S. Rolewicz

Studia Mathematica, Tome 173 (2006), p. 243-248 / Harvested from The Polish Digital Mathematics Library

Résumé

Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that $f (t x + (1 - t) y) \leq t f (x) + (1 - t) f (y) + m i n [t, (1 - t)] α (| | x - y | |)$ . Then there is a dense $G_{δ}$ -set $A_{G} \subset Ω$ such that f is Gateaux differentiable at every point of $A_{G}$ .

Publié le : 2006-01-01

Zbl 1106.46026

EUDML-ID : urn:eudml:doc:285160

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     title = {An extension of Mazur's theorem on Gateaux differentiability to the class of strongly $\alpha$ ($\cdot$)-paraconvex functions},
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     year = {2006},
     pages = {243-248},
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S. Rolewicz. An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions. Studia Mathematica, Tome 173 (2006) pp. 243-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-3-3/