In this note, we study a general version of a problem posed by Feng Qi in [10] in the context of a measured space endowed with a positive finite measure. For other studies and results, one can consult the papers [2], [3], [5], [8], [9], [12], [13] and [14]. Our basic tool is the classical Hölder inequality. By the convexity method (see [3]) we give an interpretation of the lower bound occuring ...

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.

In this paper we introduce a new extension of Hilbert's integral inequality with a best constant factor involving the hypergeometric function. The equivalent form and some examples will be given.