Displaying similar documents to “Invitation to functional means: some problems. (Invitaion to functional means some problems.)”

Extensions of convex functionals on convex cones

E. Ignaczak, A. Paszkiewicz (1998)

Applicationes Mathematicae

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We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.

A generalization of the Hahn-Banach theorem

Jolanta Plewnia (1993)

Annales Polonici Mathematici

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If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.

Convex and monotone operator functions

Jaspal Singh Aujla, H. L. Vasudeva (1995)

Annales Polonici Mathematici

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The purpose of this note is to provide characterizations of operator convexity and give an alternative proof of a two-dimensional analogue of a theorem of Löwner concerning operator monotonicity.