On a reverse Hardy–Hilbert-type integral inequality involving derivative functions of higher order

Abstract By means of the weight functions, the idea of introducing parameters and the technique of real analysis related to the beta and gamma functions, a new reverse Hardy–Hilbert-type integral inequality with the homogeneous kernel as 1 ( x + y ) λ + m + n $\frac{1}{(x + y)^{\lambda + m + n}}$ ( λ > 0 $\lambda > 0$ ) involving two derivative functions of higher order is given. As applications, the equivalent statements of the best possible constant factor related to several parameters are considered, and some particular inequalities are obtained.