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Volume 13
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10.3390/math13101563
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Article

Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications

by
László Horváth
Department of Mathematics, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary
Mathematics 2025, 13(10), 1563; https://doi.org/10.3390/math13101563
Submission received: 14 April 2025 / Revised: 2 May 2025 / Accepted: 8 May 2025 / Published: 9 May 2025
Versions Notes

Abstract

In this paper, starting from abstract versions of a result of Bennett given by Niculescu, we derive new majorization-type integral inequalities for convex functions using finite signed measures. The proof of the main result is based on a generalization of a recently discovered majorization-type integral inequality. As applications of the results, we give simple proofs of the integral Jensen and Lah–Ribarič inequalities for finite signed measures, generalize and extend known results, and obtain an interesting new refinement of the Hermite–Hadamard–Fejér inequality.
Keywords: convex functions; signed measures; Steffensen–Popoviciu and dual Steffensen–Popoviciu measures; integral Jensen and Lah–Ribarič inequalities; Hermite–Hadamard–Fejér inequality convex functions; signed measures; Steffensen–Popoviciu and dual Steffensen–Popoviciu measures; integral Jensen and Lah–Ribarič inequalities; Hermite–Hadamard–Fejér inequality

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MDPI and ACS Style

Horváth, L. Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications. Mathematics 2025, 13, 1563. https://doi.org/10.3390/math13101563

AMA Style

Horváth L. Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications. Mathematics. 2025; 13(10):1563. https://doi.org/10.3390/math13101563

Chicago/Turabian Style

Horváth, László. 2025. "Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications" Mathematics 13, no. 10: 1563. https://doi.org/10.3390/math13101563

APA Style

Horváth, L. (2025). Majorization-Type Integral Inequalities Related to a Result of Bennett with Applications. Mathematics, 13(10), 1563. https://doi.org/10.3390/math13101563

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