Publish with us
Search for Articles:

Contents

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (Online) 2616-8103 (Print)
Full-Text PDF
  • Research article

Hardy-Hilbert-Mulholland-type integral inequalities

Christophe Chesneau1
1Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France
Copyright © Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • Received: 18/11/2025
  • Accepted: 31/12/2025
  • Published: 21/01/2026

Abstract

This article introduces what we term Hardy-Hilbert-Mulholland-type integral inequalities, which unify features of Hardy-Hilbert-type and Mulholland-type integral inequalities. These inequalities are parameterized by an adjustable parameter. The obtained constant factors are derived in singular form involving a logarithmic-tangent expression, and their optimality is discussed in detail. Several new secondary inequalities are also established. Complete proofs are provided, including detailed steps and references to intermediate results.

Keywords: Hardy-Hilbert-type integral inequalities, Mulholland-type integral inequalities, optimality, Holder integral inequality, Fubini-Tonelli integral theorem, Hardy integral inequality