Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions

Year 2026, Volume: 8 Issue: 1 , 30 - 46 , 28.04.2026

Christophe Chesneau

https://doi.org/10.47087/mjm.1756359

https://izlik.org/JA99AE43LP

Abstract

This article presents two new Hilbert-type integral inequalities. These inequalities feature innovative kernel functions that combine the arctangent, maximum operator and geometric mean, depending on an adjustable parameter. We derive sharp integral bounds associated with these kernel functions and prove the optimality of the corresponding constant factors under minimal assumptions. The article provides detailed proofs and discussions that extend the classical theory of Hilbert-type inequalities to richer analytical frameworks.

Keywords

Integral inequalities , kernel functions , Holder integral inequality , Fubini-Tonelli integral theorem

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