A Weighted Generalization of Hardy–Hilbert-Type Inequality Involving Two Partial Sums

In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial differential mean value theorem, a new weighted containing two sums can be proven, which is further generalization an existing result. Based on obtained results, provide equivalent statements best possible constant factor related to several Also, illustrate how inequalities in main results generate some inequalities.