Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions
Year: 2026
Type: article
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.
Source: Maltepe Journal of Mathematics
DOI: 10.47087/mjm.1756359
Author: Christophe Chesneau
Institution: Université de Caen Normandie
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7156960898