Results 101 to 110 of about 3,706 (120)

Operator Inequalities Reverse to the Jensen Inequality

Mathematical Notes, 2001
The paper obtains reverse operator inequalities of Jensen's one as follows: Suppose that \(H\) is a Hilbert space, \(A_{i}=A_{i}^{*}\in B(H)\), \(1\leq i\leq n\), and \(aI\leq A_{i}\leq bI\) for \(i\in\{1,\cdots, n\}\). Further, suppose that \(R_{i}\in B(H)\) are arbitrary operators satisfying the condition \(\sum_{i=1}^{n} R_{i}^{*}R_{i}=I\). If \(f\)
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On Inequalities Complementary to Jensen's

Canadian Journal of Mathematics, 1983
In a paper published in 1975 [1, § 3], D. S. Mitrinovič and P. M. Vasič used the so-called “centroid method” to obtain two new inequalities which are complementary to (the discrete version of) Jensen's inequality for convex functions. In this paper we shall present a very general version of such inequalities using the same geometric ideas used in [1 ...
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An inequality for Jensen means

Nonlinear Analysis: Theory, Methods & Applications, 1991
Let \(A=A(t)\) be an \(N\)-function defining the Orlicz space \(L_ A(\Omega)\), \(\Omega\) being a bounded open set in \(R^ n\). It is known that the condition \[ C_ 1t^ p-C_ 2\leq A(t)\leq C_ 3(t^ q+1), \quad t\geq t_ 0\leqno (1) \] with ...
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Jensen’s inequality on convex spaces

Calculus of Variations and Partial Differential Equations, 2013
The author proves a Jensen inequality on \(p\)-uniformly convex spaces in terms of \(p\)-barycenters of probability measures with \((p-1)\)-th moment, with \(p\in(1,\infty)\), under a geometric condition. He also gives a Liouville-type theorem for harmonic maps described by Markov chains into a 2-uniformly convex space satisfying such a geometric ...
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On Some General Inequalities Related to Jensen’s Inequality

2008
We present several general inequalities related to Jensen's inequality and the Jensen-Steffensen inequality. Some recently proved results are obtained as special cases of these general inequalities.
Klaričić Bakula, Milica, Matić, Marko, Pečarić, Josip   +2 more
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Convexity, Jensen’s Inequality

2012
The 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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Jensen-Mercer inequality

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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On inequalities complementary to Jensen's inequality

Matematički bilten, 2008
In 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, Pečarić, Josip, Klaričić Bakula, Milica   +2 more
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An Inequality of Jensen

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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Jensen's inequality for medians

Statistics & Probability Letters, 2005
For 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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