By using the way of weight functions and technique of real analysis, a new multiple half-discrete Hilbert-type inequality with the best constant factor is given. As applications, the equivalent forms, operator expressions as well as some reverse inequalities are also considered. Mathematics subject classification (2010): 26D15, 47A07.

In the present paper, we establish an equivalent form related to a Hilbert-type integral inequality with non-homogeneous kernel and best possible constant factor. We also consider case of homogeneous as well certain operator expressions.

By using thefractal theory and the methods of weight function, a Hilbert-type fractal integral inequality and its equivalent form are given. Their constant factors are proved being the best possible, and their applications are discussed briefly.

Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 0 < q < p <∞, p > 1. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures. © 2007 Elsevier Inc. All rights reserved.

This paper deals with a relation between Hardy-Hilbert’s integral inequality and Mulholland’s integral inequality with a best constant factor, by using the Beta function and introducing a parameter λ. As applications, the reverse, the equivalent form and some particular results are considered.

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

Making use of complex analytic techniques as well methods involving weight functions, we study a few equivalent conditions Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form applications deduce homogeneous kernel, additionally consider operator expressions.

The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a general homogeneous kernel, thus generalizing a result obtained in [Namita Das and Srinibas Sahoo, A generalization of multiple Hardy-Hilbert’s integral inequality, Journal of Mathematical Inequalities, 3(1), (2009), 139–154].

In this paper, a new inequality for the weight coefficient w(q, n) in the form sin(r/p) 2mi/p + n_i/q q > I,+ I, 6 N P q is proved. This is followed by a strengthened version ofthe Hardy-I-lilben inequality.