A Reverse Hardy–Hilbert’s Inequality Containing Multiple Parameters and One Partial Sum

Abstract

In this work, by introducing multiple parameters and utilizing the Euler–Maclaurin summation formula and Abel’s partial summation formula, we first establish a reverse Hardy–Hilbert’s inequality containing one partial sum as the terms of double series. Then, based on the newly proposed inequality, we characterize the equivalent conditions of the best possible constant factor associated with several parameters. At the end of the paper, we illustrate that more new inequalities can be generated from the special cases of the reverse Hardy–Hilbert’s inequality.

Keywords

• reverse Hardy–Hilbert’s inequality
• partial sum
• multiple parameters
• best possible constant factor