Discrete Multiple Hilbert Type Inequality with Non-Homogeneous Kernel (original) (raw)

Discrete Hilbert type inequality with non-homogeneous kernel

Applicable Analysis and Discrete Mathematics, 2009

A new version of discrete Hilbert type inequality is given where the kernel function is non-homogeneous. The main mathematical tools are the representation of the Dirichlet series by means of the Laplace integral, and the H?lder inequality with non-conjugated parameters. Numerous special cases are treated and conditional best constants are discussed.

On a more accurate class of discrete Hilbert-type inequalities

Applied Mathematics and Computation, 2014

Motivated by some known results regarding a particular set of non-homogeneous kernels, in this article we study a more general class of discrete Hilbert-type inequalities. We derive a more accurate form for this class of inequalities, based on the application of the Hermite-Hadamard inequality.

Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

Rendiconti del Circolo Matematico di Palermo, 2007

In this paper we obtain an extension of discrete Hilbert's inequality, by using some numerical methods. We shall obtain, in a similar way as Yang did in , that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare our findings with existing results, known from the literature.

On Finite and Infinite Decomposition of Some Hilbert's Type Inequalities

Journal of Mathematical Extension, 2019

In this work, some Hardy-Hilbert's integral inequalities with the best possible constants is proved. Also, some finite and infinite decompositions of sometype Hardy-Hilbert's integral operators is given. Indeed, for a non-negative kernel K, two Kernels K1 and K2 is given such that TK = TK1 + TK2 and ∥TK∥ =∥TK1∥ + ∥TK2∥. So, the space of bounded linear operators is strictly convex.Also, as an application of infinite decomposition of some Hardy-Hilbert's integraloperators, the convergence of some series of hypergeometric functions is given.

New inequalities similar to Hardy-Hilbert's inequality

2010

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

Generalization of Hardy-Hilbert's Inequality and Applications

Kyungpook mathematical journal, 2010

In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered.

A Hilbert inequality and an Euler-Maclaurin summation formula

The ANZIAM Journal, 2007

We obtain a generalized discrete Hilbert and Hardy-Hilbert inequality with non-conjugate parameters by means of an Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our findings with existing results. We improve some earlier results and apply the results to some special homogeneous functions.