A Half-discrete Hardy-Mulholland-type Inequality Involving One Multiple Upper Limit Function

By constructing the kernel function and weight function and using the real analytical techniques, the half-discrete inequalities of Hardy-Mulholland type are investigated. Firstly, a half-discrete Hardy-Mulholland-type inequality containing several parameters and one multiple upper limit function is established. And then, the equivalent statements on the best possible constant factor associated with several parameters are discussed with the aid of the proposed half-discrete Hardy-Mulholland-type inequality, and several inequalities are derived via their equivalent form. The results obtained can be used to depict the structure character of Hardy-Mulholland-type inequalities for which the constant factors are best possible.