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Estimating the defect in Jensen's Inequality
Publicationes Mathematicae Debrecen, 2006Summary: 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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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. +2 more
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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. +2 more
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On a Lower Bound for the Jensen Inequality
SIAM Journal on Mathematical Analysis, 2014We 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, 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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A note on Jensen’s inequality for BSDEs
Acta Mathematica Sinica, English Series, 2009This paper is devoted to a generalization of known results on Jensen's Inequality for backward stochastic differential equations (BSDEs). Specifically, the author finds a necessary and sufficient condition on the generator \(g\) of BSDEs for which Jensen's Inequality holds for some specific convex functions.
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On Some General Inequalities Related to Jensen’s Inequality
2008We 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 +2 more
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Jensen’s inequality on convex spaces
Calculus of Variations and Partial Differential Equations, 2013The 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 Jensen’s inequality and Hölder’s inequality for g-expectation
Archiv der Mathematik, 2010The author proves that, for \(n>1\), the \(n\)-dimensional Jensen's inequality holds for the \(g\)-expectation if and only if the generator \(g \equiv g(\cdot, t, y, z)\) defined on \(\Omega \times [0, T]\times \mathbb{R} \times \mathbb{R}^d\) is independent of \(y\) and linear in \(z\). Applications are made to Minkowski's and Hölder's inequalities.
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