Related papers: Weighted Ostrowski-Gr\"uss type inequalities
In this paper weighted Dirichlet-type inequalities for the decreasing rearrangement in cylinders are proved. A weighted isoperimetric inequality is also obtained.
In this article, motivated by a work of Caffarelli and Cordoba in phase transitions analysis, we prove new weighted anisotropic Sobolev type inequalities, that is Sobolev type inequalities where different derivatives have different weight…
Some new counterparts of Bessel's inequality for orthornormal families in real or complex inner product spaces are pointed out. Applications for some Gruss type inequalities are also empahsized.
In this paper, we study several weighted norm inequalities for the Opdam--Cherednik transform. We establish different versions of the Heisenberg--Pauli--Weyl inequality for this transform. In particular, we give an extension of this…
We analyze the supports of weighted equilibrium measures in $\mathbb{C}^n$. We give explicit examples of families of compact sets which arise as the support of a weighted equilibrium measure for some admissible weight $w$. These examples…
This paper discusses the properties of a modified version of the Stancu variant Sz\'asz-Mirakjan Kantorovich type operators. We determine the order of approximation in terms of the modulus of continuity and second-order of smoothness, and…
In this paper, we establish an Orlicz log-Aleksandrov-Fenchel inequality by introducing new concepts of mixed volume measure and Orlicz multiple mixed volume measure, and using the Orlicz-Aleksandrov-Fenchel inequality. The Orlicz…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
A classical result of Aubin states that the constant in Moser-Trudinger-Onofri inequality on $\mathbb{S}^{2}$ can be imporved for furnctions with zero first order moments of the area element. We generalize it to higher order moments case.…
In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt's $A_{p}$ condition. To obtain refined version of the Jackson type inequality…
In this paper, we consider an unconventional overdetermined problem through a property of concavity, which provides some characterizations of balls via Brunn-Minkowski inequalities. In this setting, our rsults can be viewed as the…
The classical form of Gr\"uss' inequality, first published by G. Gr\"{u}ss in 1935, gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many…
We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski…
Comparing structured data from possibly different metric-measure spaces is a fundamental task in machine learning, with applications in, e.g., graph classification. The Gromov-Wasserstein (GW) discrepancy formulates a coupling between the…
For the Hardy-Littlewood maximal and Calder\'on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak…
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian measures. Unlike in the classical Brunn-Minkowski theory, the…
We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop-Gromov type. As one of the applications, we obtain an upper bound for…
In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…
We provide a simple unified approach to obtain (i) Discrete polygonal isoperimetric type inequalities of arbitrary high order. (ii) Arbitrary high order isoperimetric type inequalities for smooth curves, where both upper and lower bounds…
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…