On X-convex functions

• Autorzy: Rolewicz S.

Identyfikatory

DOI

10.14708/cm.v53i2.785

• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space. Let f(⋅) be a real valued function defined on an open convex set Ω⊂X∗, where X∗ as usual denote the conjugate space. We say that the function f(⋅) is X-convex, if there is a set Φ_f⊂X such that f(x∗)=sup_x∈Φ_{f, r}∈R^x∗(x)+r. In the paper it will be shown that if X is separable, then the function f(⋅) is Frechet differentiable on a dense G_δ set.

Słowa kluczowe

EN

X-convex functions; Frechet differentiability

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 97--99
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Rolewicz S.

• Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa 10, P.O.Box 21, Poland

Bibliografia

• [1] D. Pallaschke and S. Rolewicz, Foundation of Mathematical Optimization, Mathematics and its Applications 388, Kluwer Academic Publishers, Dordrecht / Boston / London, 1997.
• [2] S. Rolewicz, Convexity versus linearity, Transform methods and special functions 94 (1995), (eds. P.Rusev, I.Dimovski, V.Kiraykova, Science Culture Technology Publishing (Singapore ), 253 - 263.
• [3] S. Rolewicz, On Φ-differentiability of functions over metric spaces, Topological Methods of Non-linear Analysis 5 (1995), 229 - 236.