A reverse Hilbert-like optimal inequality

A Reverse Hilbert–like Optimal Inequality

We prove an inequality on positive real numbers, that looks like a reverse to the wellknown Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal. Mathematics subject classification (2010): 42A16, 42A38, 42B20.

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.

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.

Research Article A Reverse Hardy-Hilbert-Type Inequality

A multidimensional discrete Hilbert-type inequality

In this paper, by using the way of weight coecients and technique of real analysis, a multidimensionaldiscrete Hilbert-type inequality with a best possible constant factor is given. The equivalentform, the operator expression with the norm are considered.