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In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar…

Functional Analysis · Mathematics 2024-04-15 Michael Ruzhansky , Anjali Shriwastawa , Daulti Verma

In this paper, some Hermite-Hadamard type inequalities are established for harmonically $(\alpha,m)$-convex functions via fractional integrals and some Hermite-Hadamard type inequalities are obtained for these classes of functions.

Classical Analysis and ODEs · Mathematics 2015-05-12 Mehmet Kunt , İmdat İşcan

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

Classical Analysis and ODEs · Mathematics 2013-04-03 A. Saglam , M. Z. Sarikaya , H. Yildirim

The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich…

Functional Analysis · Mathematics 2025-05-14 Tohru Ozawa , Prasun Roychowdhury , Durvudkhan Suragan

We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\rm Spin^c$ Dirac operator. This…

Differential Geometry · Mathematics 2018-06-05 Volker Branding

In this paper, we characterize the sharp constant and maximizing functions for weighted Poincar\'e inequalities. These results lead to refinements of Hardy's inequality obtained by adding remainder terms involving \(L^p\) norms. We use…

Analysis of PDEs · Mathematics 2025-03-17 Lorenzo D'Arca

The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…

Classical Analysis and ODEs · Mathematics 2023-02-27 Lars-Erik Persson , Natasha Samko , George Tephnadze

We consider Hardy-Rellich inequalities and discuss their possible improvement. The procedure is based on decomposition into spherical harmonics, where in addition various new inequalities are obtained (e.g. Rellich-Sobolev inequalities). We…

Analysis of PDEs · Mathematics 2007-05-23 A. Tertikas , N. B. Zographopoulos

We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $\Delta_{p}u := \Div(\abs{\nabla u}^{p-2}\nabla u)$. Namely, if $\rho$ is a…

Analysis of PDEs · Mathematics 2013-04-16 Lorenzo D'Ambrosio , Serena Dipierro

By the coupling method, we establish the Harnack inequalities, derivative formula and Driver's integration by parts formula for the stochastic Klein-Gordon type equations in the interval. We provide a detailed discussion about the nonlinear…

Probability · Mathematics 2013-11-01 Zhang Shao-Qin

In the paper, the authors introduce a notion "$(\alpha,m)$-GA-convex functions" and establish some integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-GA-convex functions.

Classical Analysis and ODEs · Mathematics 2014-12-02 Ai-Ping Ji , Tian-Yu Zhang , Feng Qi

This paper is devoted to Hardy type inequalities with remainders for compactly supported smooth functions on open sets in the Euclidean space. We establish new inequalities with weight functions depending on the distance function to the…

Functional Analysis · Mathematics 2020-03-20 Makarov R. V. , Nasibullin R. G

In this paper, new integral inequalities of Hadamard type involving several differentiable \Phi-r-convex functions are given.

Classical Analysis and ODEs · Mathematics 2012-03-13 Mehmet Zeki Sarikaya , Hatice Yaldiz , Hakan Bozkurt

In this paper we introduce operator s-convex func- tions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

Functional Analysis · Mathematics 2014-07-10 Amir Ghasem Ghazanfari

In this paper several inequalities of the right-hand side of Hermite-Hadamard inequality are obtained for the class of functions whose derivatives in absolutely value at certain powers are ({\alpha},m)-convex.Some applications to special…

Classical Analysis and ODEs · Mathematics 2013-04-19 Imdat Işcan

A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type…

General Relativity and Quantum Cosmology · Physics 2014-10-07 Ion I. Cotaescu

We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with…

Analysis of PDEs · Mathematics 2021-04-06 Megumi Sano

In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, H\"{o}lder's inequality and Cauchy's…

Classical Analysis and ODEs · Mathematics 2011-03-21 Nicuşor Minculete , Shigeru Furuichi

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

Functional Analysis · Mathematics 2014-09-24 Silvestru Sever Dragomir

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