An Extension of the Hilbert's Integral Inequality

Abstract

It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters m   (m∈N) and λ   (λ>0). The constant factors expressed by the Euler number and π as well as by the Bernoulli number and π, respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.