Related papers: On Pompeiu-Chebyshev functional and its generaliza…

We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are…

The classical form of Gr\"{u}ss' inequality was first published by G. Gr\"{u}ss in 1935 and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. After that many variants…

In this article we present both the discrete and the integral form of Cauchy-Bunyakovsky-Schwarz (CBS) inequality, some important generalizations in the n-dimensional Euclidean space and in linear subspaces of it, as well as the…

In this work, considering a general subclass of bi-univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

In the present paper, a new subclass of analytic and bi-univalent functions by means of Chebyshev polynomials is introduced. Certain coefficient bounds for functions belong to this subclass are obtained. Furthermore, the Fekete-Szego…

In this work a mean value theorem of Pompeiu's type for functions of two variables is presented. Other related results are given as well.

Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third…

Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.

In this paper, new versions of Chebyshev's, Minkowski's and Holder's type inequalities are studied by using a monotone measure-base universal integral on an arbitrary measurable space. This paper generalizes some previous results obtained…

We obtain the decay bounds for Chebyshev series coefficients of functions with finite Vitali variation on the unit square. A generalization of the well known identity, which relates exact and approximated coefficients, obtained using the…

A variant of the well-known Chebyshev inequality for scalar random variables can be formulated in the case where the mean and variance are estimated from samples. In this paper we present a generalization of this result to multiple…

The main objective of this paper is to obtain generalization of some Gruss-type inequalities in case of functional bounds by using a generalized Katugampola fractional integral.

In this paper we discuss the generalizations of the concept of Chebyshev's bias from two perspectives. First we give a general framework for the study of prime number races and Chebyshev's bias attached to general $L$-functions satisfying…

The Chebyshev polynomials are utilized in this study to define the subclass of the bi-univalent function. Also, Chebyshev polynomial bounds and Fekete-Szego inequalities for functions defined in the classes are established.

Generalizations of Ostrowski type inequality for functions of Lipschitzian type are established. Applications in numerical integration and cumulative distribution functions are also given.

In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.

In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.

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

In this paper we demonstrate that a well known linear inequality method developed for rational Chebyshev approximation is equivalent to the application of the bisection method used in quasiconvex optimisation. Although this correspondence…

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…