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Related papers: A Generalization of Hermite-Hadamard's Inequality

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This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein…

Functional Analysis · Mathematics 2017-01-04 Erik Thomas

The Hermite polynomials are ubiquitous but can be difficult to work with due to their unwieldy definition in terms of derivatives. To remedy this, we showcase an underappreciated Gaussian integral formula for the Hermite polynomials, which…

Probability · Mathematics 2025-11-18 Mihai Nica , Janosch Ortmann

In this study, we establish and generalize some inequalities of Hadamard and Simpson type based on s-convexity in the second sense. Some applications to special means of positive real numbers are also given and generalized. Examples are…

Classical Analysis and ODEs · Mathematics 2013-04-23 Mevlut Tunc

In this paper, we prove some new inequalities of Hadamard-type for s-convex functions on the co-ordinates.

Classical Analysis and ODEs · Mathematics 2012-03-22 M. Emin Ozdemir , Mevlut Tunc , Ahmet Ocak Akdemir

We establish a general criterion for the validity of inequalities of the following form: A certain convex combination of the values of a convex function at n points and of its value at a weighted mean of these n points is always greater or…

Functional Analysis · Mathematics 2008-03-21 Darij Grinberg

Using methods of weight functions, techniques of real analysis as well as the Hermite-Hadamard inequality, a half-discrete Hardy-Hilbert-type inequality with multi-parameters and a best possible constant factor related to the Hurwitz zeta…

Classical Analysis and ODEs · Mathematics 2015-12-16 Michael Th. Rassias , Bicheng Yan

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

Classical Analysis and ODEs · Mathematics 2012-07-12 Imdat Iscan

The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional $p-$Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and…

Classical Analysis and ODEs · Mathematics 2013-09-20 Riku Klén , Matti Vuorinen , Xiaohui Zhang

In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators.…

Classical Analysis and ODEs · Mathematics 2021-11-23 Peng Chen , Jinsen Xiao

Famous Redheffer's inequality is generalized to a class of anti-periodic functions. We apply the novel inequality to the generalized trigonometric functions and establish several Redheffer-type inequalities for these functions.

Classical Analysis and ODEs · Mathematics 2021-12-28 Shimpei Ozawa , Shingo Takeuchi

In this paper, we not only give the extensions of the results given in [7] by Gill et al. for log-convex functions, but also obtain some new Hadamard type inequalities for log-convex, m-convex and (alpha,m)-convex functions.

Functional Analysis · Mathematics 2011-04-01 Erhan Set , M. Emin Ozdemir , Sever S. Dragomir

In this paper, we extend some estimates of the right and left hand side of a Hermite-Hadamard type inequality for nonconvex functions whose derivatives absolute values are \Phi-convex and quasi-\Phi-convex was introduced by Noor in Noor1.

Classical Analysis and ODEs · Mathematics 2013-04-03 Mehmet Zeki Sarikaya , Hakan Bozkurt , Necmettin Alp

The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain…

General Mathematics · Mathematics 2020-07-22 Asha B. Nale , Satish K. Panchal , Vaijanath L. Chinchane

The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…

Metric Geometry · Mathematics 2025-06-04 Dylan Langharst , Eli Putterman

In this paper, we prove an operator version of the Jensen's inequality and its converse for $h$-convex functions. We provide a refinement of the Jensen type inequality for $h$-convex functions. Moreover, we prove the Hermite-Hadamard's type…

Functional Analysis · Mathematics 2022-01-19 Ismail Nikoufar , Davuod Saeedi

We establishe an affine Hardy-Littlewood-Sobolev inequality concerning two different functions which is stronger than the classical Hardy-Littlewood-Sobolev inequality. Furthermore, we also prove reverse inequalities for the new…

Functional Analysis · Mathematics 2025-08-05 Youjiang Lin , Jinghong Zhou , Jiaming Lan

In this paper we establish Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense and concave.

Classical Analysis and ODEs · Mathematics 2013-04-01 Erhan Set , M. Emin Ozdemir , M. Zeki Sarikaya , Filiz Karakoc

Hardy's inequality for Laguerre expansions of Hermite type with the index $\al\in(\{-1/2\}\cup[1/2,\infty))^d$ is proved in the multi-dimensional setting with the exponent $3d/4$. We also obtain the sharp analogue of Hardy's inequality with…

Classical Analysis and ODEs · Mathematics 2018-10-10 Paweł Plewa

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

Classical Analysis and ODEs · Mathematics 2011-01-05 M. Emin Ozdemir , Ahmet Ocak Akdemir , Havva Kavurmaci , Merve Avci

In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.

Classical Analysis and ODEs · Mathematics 2022-05-03 Changyu Ren