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Convexity, Jensen’s Inequality
2012The main purpose of this section is to acquaint the reader with one of the most important theorems, that is widely used in proving inequalities, Jensen’s inequality. This is an inequality regarding so-called convex functions, so firstly we will give some definitions and theorems whose proofs are subject to mathematical analysis, and therefore we’ll ...
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2007
We consider the Jensen-Mercer inequality in various spaces and for several types real valued functions. This also enables us to define a variety of weighted means and to explore their relationships. Besides of the Mercer's variant of Jensen's inequality, we show analogous variant of the Jensen-Steffensen inequality, from which similar variants of some ...
Matković, Anita, Pečarić, Josip
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We consider the Jensen-Mercer inequality in various spaces and for several types real valued functions. This also enables us to define a variety of weighted means and to explore their relationships. Besides of the Mercer's variant of Jensen's inequality, we show analogous variant of the Jensen-Steffensen inequality, from which similar variants of some ...
Matković, Anita, Pečarić, Josip
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On inequalities complementary to Jensen's inequality
Matematički bilten, 2008In this paper we give generalizations of two complementary inequalities proved by Pečarić and Mesihović. We also show that a generalization of Niculescu's inequality obtained by M. Dincă, S. Rădulescu and M. Bencze is a simple consequence of an older theorem proved by Pečarić and Mesihović.
Matić, Marko +2 more
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The American Mathematical Monthly, 1946
(1946). An Inequality of Jensen. The American Mathematical Monthly: Vol. 53, No. 9, pp. 501-505.
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(1946). An Inequality of Jensen. The American Mathematical Monthly: Vol. 53, No. 9, pp. 501-505.
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Jensen's inequality for medians
Statistics & Probability Letters, 2005For any random variable \(X\) with finite expectation \(EX\) and for any convex function \(f\), the well-known Jensen's inequality \(f(EX) \leq Ef(X)\) holds, playing a significant role in probability and statistics theory. The aim of this note is to present an analogue of Jensen's inequality, where expectation is replaced by median.
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Convexity and Jensen's Inequality
The American Mathematical Monthly, 1975(1975). Convexity and Jensen's Inequality. The American Mathematical Monthly: Vol. 82, No. 10, pp. 1005-1005.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Operator Inequalities Associated with Jensen’s Inequality
2000We give a survey of various operator inequalities associated with Jensen’s inequality and study the class of operator convex functions of several variables. Related questions are considered.
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2006
Izučavana su poopćenja i profinjenja Jensen-Mercerove nejednakosti za raznovrsne klase realnih funkcija, te njihovi analogoni za različite općenitije strukture i prikladne uređaje. Budući da ona omogućuju definiranje više klasa težinskih sredina, proučavani su i međusobni odnosi tih sredina.
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Izučavana su poopćenja i profinjenja Jensen-Mercerove nejednakosti za raznovrsne klase realnih funkcija, te njihovi analogoni za različite općenitije strukture i prikladne uređaje. Budući da ona omogućuju definiranje više klasa težinskih sredina, proučavani su i međusobni odnosi tih sredina.
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