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Displaying similar documents to “On a Jensen-Mercer operator inequality.”

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.

Bounds for Convex Functions of Čebyšev Functional Via Sonin's Identity with Applications

Silvestru Sever Dragomir (2014)

Communications in Mathematics

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Some new bounds for the Čebyšev functional in terms of the Lebesgue norms f - 1 b - a ∫ a b f ( t ) d t [ a , b ] , p and the Δ -seminorms ∥ f ∥ p Δ : = ∫ a b ∫ a b | f ( t ) - f ( s ) | p d t d s 1 p are established. Applications for mid-point and trapezoid inequalities are provided as well.