Predrag Vuković

On a multidimensional version of the Hilbert-type inequality in the whole plane

The main objective of this paper is a study of some new multidimensional Hilbert-type inequalities with a general homogeneous kernel in the whole plane. We derive a pair of equivalent inequalities, and we also establish the conditions under which the constant factors included in the obtained inequalities are the best possible. Some applications in particular settings are also considered.MSC:26D15.

On a more accurate class of discrete Hilbert-type inequalities

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.

Hardy-Hilbert-Type Inequalities with a Homogeneous Kernel in Discrete Case

The main objective of this paper is a study of some new generalizations of Hilberts and Hardy-Hilberts type inequalities. We apply our general results to homogeneous functions. We shall obtain, in a similar way as Yang did in(2009), that the constant factors are the best possible when the parameters satisfy appropriate conditions.

Multidimensional Hilbert-Type Inequalities with a Homogeneous Kernel

We consider the Hilbert-type inequalities with nonconjugate parameters. The obtaining of the best possible constants in the case of nonconjugate parameters remains still open. Our generalization will include a general homogeneous kernel. Also, we obtain the best possible constants in the case of conjugate parameters when the parameters satisfy appropriate conditions. We also compare our results with some known results.

Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

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 [10], 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.