On a New Extended Hardy–Hilbert’s Inequality with Parameters

Abstract

In this paper, by introducing parameters and weight functions, with the help of the Euler–Maclaurin summation formula, we establish the extension of Hardy–Hilbert’s inequality and its equivalent forms. The equivalent statements of the best possible constant factor related to several parameters are provided. The operator expressions and some particular cases are also discussed.

On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums

“…Recently, Yang and Wu et al [28,29] gave a reverse half-discrete Hardy-Hilbert's inequality and an extended Hardy-Hilbert's inequality. For these inequalities, the equivalent statements of the best possible constant factor related to several parameters were also discussed therein.…”