Two new forms of Hilbert integral inequality

A new Hilbert-type integral inequality and the equivalent form

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.

A Hilbert Integral-Type Inequality with Parameters

A Reverse Hardy-hilbert-type Integral Inequality

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.

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 a Generalization of Hilbert-Type Integral Inequality