On Two One-Parameter Variants of the Hardy-Hilbert Integral Inequality

Abstract

This article establishes two new one-parameter variants of the Hardy-Hilbert integral inequality. These results are derived by modifying an existing framework that incorporates the absolute difference between unity and the product of two variables, raised to an adjustable power parameter. By employing two distinct approaches, we obtain different weighted integral norms for the primary functions. The proofs are presented in comprehensive detail and are entirely self-contained.