Affiliation:
1. Institute of Applied Mathematics, Longyan University, Longyan 364012, China
2. School of Mathematics, Guangdong University of Education, Guangzhou 510303, China
Abstract
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 summation formula, and differential mean value theorem, a new weighted Hardy–Hilbert-type inequality containing two partial sums can be proven, which is a further generalization of an existing result. Based on the obtained results, we provide the equivalent statements of the best possible constant factor related to several parameters. Also, we illustrate how the inequalities obtained in the main results can generate some new Hardy–Hilbert-type inequalities.
Funder
Natural Science Foundation of Fujian Province of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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