On a Reverse Half-Discrete Hilbert-Type Inequality with the General Homogeneous Kernel as Well as Multiple Lower Limit Function and Remainder Sum

Abstract

By means of the weight functions, the idea of introduced parameters, and the reverse Hardy’s integral inequality, an extended reverse Hardy-type inequality is obtained, and then a new reverse half-discrete Hilbert-type inequality with the general homogeneous kernel, as well as multiple lower limit function and remainder sum, is given. The equivalent statements of the best value related to several parameters are considered. As applications, the equivalent forms and some particular examples are provided.