By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.

Hilbert and Hardy-Hilbert type inequalities see 1 are very significant weight inequalities which play an important role in many fields of mathematics. Although classical, such inequalities have attracted the interest of numerous mathematicians and have been generalized in many different ways. Also the numerous mathematicians reproved them using various techniques. Some possibilities of generali...

The classical Bohr inequality says that |a+b| ≤ p|a|+q|b| for all scalars a, b and p, q > 0 with 1 p + 1 q = 1. The equality holds if and only if (p− 1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogr...

where the constant factor π 1 is the best possible. This is the famous Hilbert’s integral inequality see 1, 2 . Owing to the importance of the Hilbert’s inequality and the Hilberttype inequality in analysis and applications, some mathematicians have been studying them. Recently, various improvements and extensions of 1.1 appear in a great deal of papers see 3–11 , etc. . Specially, Gao and Hsu ...

We give some inequalities related to a large class of operator norms, the so-called Q norms, for a (not necessary commutative) family of bounded linear operators acting on a Hilbert space that are related to the classical Schwarz inequality. Applications for vector inequalities are also provided.