Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions
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
References
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Details
Primary Language
English
Subjects
Mathematical Methods and Special Functions
Journal Section
Research Article
Authors
Publication Date
April 28, 2026
Submission Date
August 1, 2025
Acceptance Date
February 17, 2026
Published in Issue
Year 2026 Volume: 8 Number: 1
