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About the sharpness of the Jensen inequality [PDF]
Journal of Inequalities and Applications, 2018 The main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green functions and considering the case of the real Stieltjes measure, not ...
Ðilda Pečarić +2 more
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An equivalent condition to the Jensen inequality for the generalized Sugeno integral [PDF]
Journal of Inequalities and Applications, 2017 For the classical Jensen inequality of convex functions, i.e., H ( 1 μ ( D ) ∫ D f d μ ) ≤ 1 μ ( D ) ∫ D H ∘ f d μ , $$\begin{aligned} H \biggl(\frac{1}{\mu(D)} \int_{D}f\,d\mu \biggr)\leq\frac{1}{\mu (D)} \int_{D} H\circ f\,d\mu, \end{aligned}$$ an ...
Mohsen Jaddi +3 more
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Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure [PDF]
Journal of Inequalities and Applications, 2017 We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained ...
Rozarija Mikić +2 more
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Refinement of the Jensen integral inequality [PDF]
Open Mathematics, 2016 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.
Sever Dragomir Silvestru +2 more
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Fractal and FractionalThis paper derives the sharp bounds for Hermite–Hadamard inequalities in the context of Riemann–Liouville fractional integrals. A generalization of Jensen’s inequality called the Jensen–Mercer inequality is used for general points to find the new and ...
Muhammad Aamir Ali +3 more
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Advancements in integral inequalities of Ostrowski type via modified Atangana-Baleanu fractional integral operator [PDF]
HeliyonConvexity and fractional integral operators are closely related due to their fascinating properties in the mathematical sciences. In this article, we first establish an identity for the modified Atangana-Baleanu (MAB) fractional integral operators. Using
Gauhar Rahman +4 more
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Jensen inequality and the second law [PDF]
Physics Letters, Section A: General, Atomic and Solid State Physics, 2020 Jensen's Inequality (JIEQ) has proved to be a major tool to prove the consistency of various fluctuation theorems with the second law in microscopic thermodynamics. We show that the situation is far from clear and the reliance on the JIE may be quite misleading in general.
exaly +4 more sources
On a Converse of Jensen's Discrete Inequality
Journal of Inequalities and Applications, 2009 We give the best possible global bounds for a form of discrete Jensen's inequality. By some examples the fruitfulness of this result is shown.
Slavko Simic
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Quantile Jensen’s inequalities [PDF]
Journal of Inequalities and Applications, 2021 AbstractQuantiles of random variable are crucial quantities that give more delicate information about distribution than mean and median and so on. We establish Jensen’s inequality for q-quantile ($q\geq 0.5$ q ≥ 0.5 ) of a random variable, which includes as a special case Merkle ...
Mu Zhao +4 more
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On the refinements of Jensen Mercer's inequality
Journal of Numerical Analysis and Approximation Theory, 2012 In this paper we give refinements of Jensen-Mercer's inequality and its generalizations and give applications for means. We prove \(n\)-exponential convexity of the functions constructed from these refinements. At the end we discuss some examples.
M. Adil Khan, Asif R. Khan, J. Pečarić
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