A note on Hilbert's inequality

On a decomposition of Hardy--Hilbert's type inequality

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.

On a New Reverse Hilbert\'s Type Inequality

In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.

On Further Analogs of Hilbert's Inequality

By introducing the function | lnx − ln y|/(x + y + |x − y|), we establish new inequalities similar to Hilbert's type inequality for integrals. As applications, we give its equivalent form as well.

On further strengthened Hardy-Hilbert's inequality

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...