A Hardy–Hilbert-type integral inequality involving two multiple upper-limit functions

Abstract By means of the weight functions, idea introducing parameters and technique real analysis, a new Hardy–Hilbert-type integral inequality with homogeneous kernel $\frac{1}{(x + y)^{\lambda}}\ (\lambda > 0)$ 1(x+y)λ(λ>0) involving two multiple upper-limit functions is obtained. The equivalent statements best possible constant factor related to beta gamma are considered. As applications, forms case nonhomogeneous deduced. Some particular inequalities operator expressions provided.