Related papers: New Inequalities of Gruss Type for the Stieltjes I…
In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.
Integrating with respect to functions which are constant on intervals whose bounds are discontinuity points (of those functions) is frequent in many branches of Mathematics, specially in stochastic processes. For such functions and alike…
In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove…
In this paper, we improve and further generalize some Ostrowski-Gr\"uss type inequalities for the fractional integrals by using new Montogomery identities.
A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Gruss type results are also provided.
A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Gruss type inequalities are also provided.
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…
The median principle is applied for different integral inequalities of Gruss and Ostrowski type.
We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…
It is known in the case of the Stieltjes transform that evaluating the integral by expanding the kernel of transformation followed by term by term integration leads to an infinite series of divergent integrals. Moreover, it is known that…
We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillations and the leading order of growth are provided. The formula…
In the paper, by using Lupa\c{s} integral inequality, the authors find some new inequalities for the complete elliptic integrals of the first and second kinds. These results improve some known inequalities.
We study in this article a new pointwise estimate for ''rough'' singular integral operators. From this pointwise estimate we will derive Sobolev type inequalities in a variety of functional spaces.
Inter alia, we present a Fourier series involving the generalised Stieltjes constants.
The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical…
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,…
We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.
In this paper, some new integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions are established and some applications to special means of positive real numbers are also given.
We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.