Asia Mathematika, Vol 9, issue 2, pages: 21-35.

A new two-parameter optimal integral inequality of the Hardy-Hilbert type

Christophe Chesneau
Department of Mathematics, LMNO, University of Caen-Normandie, Caen, France.

Received: 04 Jun 2025 | Accepted: 19 Jul 2025 | Final Version: 31 Aug 2025

Abstract

This paper introduces a flexible integral inequality with two adjustable parameters, thereby generalizing the classical Hardy-Hilbert integral inequality. We determine the conditions under which the inequality is optimal by identifying the relevant parameter configurations. Furthermore, we derive several related integral inequalities involving a single function. Throughout the analysis, we provide comprehensive and rigorous proofs to ensure transparency and precision.

Keywords:
Integral inequalities, Hardy-Hilbert-type integral inequalities, power functions, optimal constants.

1. Introduction

Exploring integral inequalities is a fundamental aspect of mathematical analysis, particularly in the study of the properties of integral operators and the structure of function spaces...

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