Maltepe Journal of Mathematics 2667-7660 Hüseyin ÇAKALLI 10.47087/mjm.1756359 Mathematical Methods and Special Functions Matematiksel Yöntemler ve Özel Fonksiyonlar Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions https://orcid.org/0000-0002-1522-9292 Chesneau Christophe Université de Caen-Normandie 04 28 2026 8 1 30 46 08 01 2025 02 17 2026 Copyright © 2019, Maltepe Journal of Mathematics 2019 Maltepe Journal of Mathematics

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.

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