Related papers: Inegalit\u{a}\c{t}i de tip Chebyshev-Gr\"uss pentr…
The aim of this paper is to establish Tur\'an -type inequality for the Hahn-Exton $q$-Bessel functions. The result is obtained by the use of limit transition.
In this paper, we introduce a new sequence of operators based on the Gr\"unwald interpolation operators on Chebyshev nodes on the space $L^p[0,{\pi}]$. The operators we consider are integral variants of the Gr\"unwald interpolation…
The main study of this article is the characterization of Richard's inequality, because it is closely related to Buzano's inequality. Finally, we present a newapproach for Richard's inequality, where we use the Selberg operator.
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D.S. Mitrinovic, who left us 25 years ago. His significant influence to…
In this paper first we survey the Tur\'an type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Tur\'an type inequalities for Bessel functions of the first kind to real…
In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . Some well known inequalities can be derived as special cases. In addition, perturbed…
We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
Askey and Gasper (1976) proved a trigonometric inequality which improves another trigonometric inequality found by M. S. Robertson (1945). Here these inequalities are reformulated in terms of the Chebyshev polynomial of the first kind $T_n$…
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider H\"older-,…
We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…
For a probability measure $\mu$ and for square integrable fields $(\mathscr{A}_t)$ and $(\mathscr{B}_t)$ ($t\in\Omega$) of commuting normal operators we prove Landau type inequality \llu\int_\Omega\mathscr{A}_tX\mathscr{B}_td\mu(t)-…
Bunyakovsky's integral inequality (1859) is one of the familiar tools of modern Analysis. We try and understand what Bunyakovsky did, why he did it, why others did not follow the same path, and explore some of the mathematical…
50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the corresponding equality cases as well as the…
In this paper we show a new inequality which generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second…
In this paper, we study Bessel operators and Bessel Laplace equations studied by Weinstein, Huber, and related the harmonic function theory introduced by Muckenhoupt--Stein. We establish the Moser type inequality for these harmonic…
In this paper, we establish separate necessary and sufficient John-Nirenberg (JN) type inequalities for functions in $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ which imply Gagliardo-Nirenberg (GN) type inequalities in…
Bell's inequality for continuous-variable bipartite systems is studied. The inequality is expressed in terms of pseudo-spin operators and quantum expectation values are calculated for generic two-mode squeezed states characterized by a…
Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in in 1940s. The original versions of these sums were introduced by R.J.Evans in 1981 and, following an elegant idea of G.W.Anderson in 1991 they were…