Results 251 to 260 of about 4,698 (283)

On the \(h\)-Jensen's operator inequality

2022
Summary: In this paper, we prove Jensen's operator inequality for an \(h\)-convex function and we point out the results for classes of continuous fields of operators. Also, some generalizations of Jensen's operator inequality and some properties of the \(h\)-convex function are given.
Hashemi Karouei, S. S., Asgari, M. S., Shah Hosseini, M., Ghafoori Adl, N.   +3 more
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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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Jensen’s Inequality

2018
Historical origins. Jensen’s inequality is named after the Danish mathematician Johan Ludwig William Valdemar Jensen, born 8 May 1859 in Nakskov, Denmark, died 5 March 1925 in Copenhagen, Denmark.
Hayk Sedrakyan, Nairi Sedrakyan
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Converse Jensen–Steffensen inequality

Aequationes mathematicae, 2011
In this paper we prove a converse to the Jensen-Steffensen inequality and two inequalities complementary to the Jensen-Steffensen inequality. We apply so called exp-convex method in order to interpret our results in the form of exponentially convex functions. The outcome is a number of new interesting inequalities as well as some new Cauchy type means.
Klaričić Bakula, Milica, Ivelić Bradanović, Slavica, Pečarić, Josip   +2 more
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Jensen's inequality

Mathematical Notes of the Academy of Sciences of the USSR, 1987
Translation from Mat. Zametki 41, No.6, 798-806 (Russian) (1987; Zbl 0627.26007).
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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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Estimating the defect in Jensen's Inequality

Publicationes Mathematicae Debrecen, 2006
Summary: We consider how much the difference of the two sides of Jensen's inequality might be. It has a connection with Grüss' inequality.
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Refining Jensen's inequality

2004
Summary: A refinement of Jensen's inequality is presented. An extra term makes the inequality tighter when the convex function is ``superquadratic'', a strong convexity-type condition is introduced here. This condition is shown to be necessary and sufficient for the refined inequality.
Jameson, Graham J. O., Abramovich, Shoshana, Sinnamon, Gord   +2 more
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On a Lower Bound for the Jensen Inequality

SIAM Journal on Mathematical Analysis, 2014
We present an improvement to the Jensen inequality for certain convex functions $\phi$ on $(0\,\infty)$. This implies finding a nonzero lower bound for the Jensen gap. In particular, just as the Jensen inequality becomes an equality when $\phi$ is linear, for the new inequality we obtain an equality also when $\phi$ is quadratic.
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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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