Displaying similar documents to “Convexly totally bounded and strongly totally bounded sets. Solution of a problem of Idzik”

On the second order derivatives of convex functions on the Heisenberg group

Cristian E. Gutiérrez, Annamaria Montanari (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous ℋ –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives...

The Space of Differences of Convex Functions on [0, 1]

Zippin, M. (2000)

Serdica Mathematical Journal

Similarity:

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany). The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1] ...

Pairs of sets with convex union.

Ryszard Urbanski (1997)

Collectanea Mathematica

Similarity:

In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.

A minimax inequality with applications to existence of equilibrium point and fixed point theorems

Xie Ding, Kok-Keong Tan (1992)

Colloquium Mathematicae

Similarity:

Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence...