A new reverse Hardy–Hilbert inequality with the power function as intermediate variables

Abstract

Abstract In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients and use them to establish a reverse Hardy–Hilbert inequality with the power function as intermediate variables. Then, we obtain the equivalent forms and some equivalent statements of the best possible constant factor related to several parameters. Finally, we illustrate how the obtained results can generate some particular reverse Hardy–Hilbert inequalities.

Keywords

• Weight coefficient
• Hardy–Hilbert inequality
• Equivalent statement
• Parameter
• Power function
• Reverse