By using Euler-Maclaurin's summation formula and the way of real analysis, a more accurate multipleHilbert-type inequality and the equivalent form are given. We also prove that the same constantfactor in the equivalent inequalities is the best possible.

was first discovered by M. Petrovich in 1917, [5] (see [4, p. 492]) and subsequently was rediscovered by other authors, including J. Karamata [2, p. 300 – 301], H.S. Wilf [6], and in an equivalent form by M. Marden [3]. The first to consider the problem of obtaining reverses for the triangle inequality in the more general case of Hilbert and Banach spaces were J.B. Diaz and F.T. Metcalf [1] who...

In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results known We also get classical Hardy–Hilbert inequality.

Abstract By using the idea of introducing parameters and weight coefficients, a new reverse discrete Mulholland-type inequality in whole plane with general homogeneous kernel is given, which an extension Mulholland inequality. The equivalent forms are obtained. statements best possible constant factor related to several few applied examples presented.

In this paper, by introducing some parameters and by employing a sharpening of Hölder’s inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder’s theorem is given.

In this paper, we prove a variant of a general Hardy-Knopp type inequality. We also formulate a convolution inequality in the language of topological groups. By our main results we obtain a general form of multidimensional strengthened Hardy and Pólya-Knopp-type inequalities.

Abstract We discuss when an operator T, subject to a rather general inequality in hereditary form, admits unitarily equivalent functional model of Agler type the reproducing kernel Hilbert space associated inequality. The need not be Nevanlinna-Pick type. define defect D our context and structure spectrum T is finite rank. As second application, some consequences concerning ergodic behavior are...

Abstract We consider the Hilbert-type operator defined by $$\begin{aligned} H_{\omega }(f)(z)=\int _0^1 f(t)\left( \frac{1}{z}\int _0^z B^{\omega }_t(u)\,du\right) \,\omega (t)dt, \end{aligned}$$ H ω ( f ...