Displaying similar documents to “Extensions and improvements of Sherman’s and related inequalities forn-convex functions”

Characterization of convex functions

Jacek Tabor, Józef Tabor (2009)

Studia Mathematica

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There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.

A general framework for extending means to higher orders

Jimmie Lawson, Yongdo Lim (2008)

Colloquium Mathematicae

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Although there is an extensive literature on various means of two positive operators and their applications, these means do not typically readily extend to means of three and more operators. It has been an open problem to define and prove the existence of these higher order means in a general setting. In this paper we lay the foundations for such a theory by showing how higher order means can be inductively defined and established in general metric spaces, in particular, in convex metric...

Definable quantifiers in second order arithmetic and elementary extensions of ω-models

Wojciech Guzicki

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CONTENTS0. Introduction and terminology..............................................................51. Quantifiers and elementary extensions..............................................82. Elementary extensions of countable models of set theory................153. Interpretations of set theory in extensions of A₂...............................214. Definable quantifiers in models of A₂...............................................325. Elementary generic extensions........................................................40References..........................................................................................50 ...

On Convex Sets with Convex-Hereditary CEP

Tadeusz Dobrowolski (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.

Refinement of the Jensen integral inequality

Silvestru Sever Dragomir, Muhammad Adil Khan, Addisalem Abathun (2016)

Open Mathematics

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In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.