A parametric smooth variational principle and support properties of convex sets and functions
Articolo
Data di Pubblicazione:
2009
Citazione:
A parametric smooth variational principle and support properties of convex sets and functions / L. Vesely. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 350:2(2009), pp. 550-561.
Abstract:
We show a modified version of Georgiev's parametric smooth variational principle, and we use it to derive new support properties of convex functions and sets. For example, our results imply that, for any proper l.s.c. convex nonaffine function h on a Banach space Y, D(∂h) is pathwise connected and R(∂h) has cardinality at least continuum. If, in addition, Y is Fréchet-smooth renormable, then R(∂h) is pathwise connected and locally pathwise connected. Analogous properties for support points and normalized support functionals of closed convex sets are proved; they extend and strengthen recent results proved by C. De Bernardi and the author for bounded closed convex sets.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Convex set ; Support point ; Support functional ; Smooth variational principle ; Bishop–Phelps theorem
Elenco autori:
L. Vesely
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