Abstract By applying the weight functions, idea of introducing parameters and technique real analysis, a new multiple Hilbert-type integral inequality involving upper limit functions is given. The constant factor related to gamma function proved be best possible in condition. A corollary about case nonhomogeneous kernel some particular inequalities are obtained.

Abstract By means of the weight functions, idea introducing parameters and technique real analysis, a new Hardy–Hilbert-type integral inequality with homogeneous kernel $\frac{1}{(x + y)^{\lambda}}\ (\lambda &gt; 0)$ 1(x+y<m...

Making use of complex analytic techniques as well methods involving weight functions, we study a few equivalent conditions Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form applications deduce homogeneous kernel, additionally consider operator expressions.

In this paper, by the use of the methods of weight functions and technique of real analysis, a more accurate half-discrete Hilbert-type inequality with a general non-homogeneous kernel and a best possible constant factor is given. The equivalent forms and some reverses are obtained. We also consider the operator expressions with the norm and some particular examples.