A novel approach to refining discrete Jensen's inequality and its applications

Sumaira Sahar; Muhammad Adil Khan; Hidayat Ullah; Nannan Fang; Khalid A. Alnowibet; Sumaira Sahar; Muhammad Adil Khan; Hidayat Ullah; Nannan Fang; Khalid A. Alnowibet

doi:10.3934/math.20251147

AIMS Mathematics

2025, Volume 10, Issue 11: 26058-26076. doi: 10.3934/math.20251147

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Research article Special Issues

A novel approach to refining discrete Jensen's inequality and its applications

1.
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
2.
Department of General Education, Anhui Xinhua University, Hefei, 230088, China
3.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 07 August 2025 Revised: 17 October 2025 Accepted: 30 October 2025 Published: 11 November 2025
MSC : 26A51, 26D15, 68P30

The aim of this article is to introduce a novel and logically motivated approach that successfully yields a new refinement of the discrete form of Jensen's inequality. The proposed refinement is further applied to several important areas, including inequalities involving means, Hölder's inequality, and information theory, thereby demonstrating both the theoretical strength and practical utility of the result.
- Jensen's inequality,
- refinement,
- convex function,
- power mean,
- information theory,
- Hölder inequality
Citation: Sumaira Sahar, Muhammad Adil Khan, Hidayat Ullah, Nannan Fang, Khalid A. Alnowibet. A novel approach to refining discrete Jensen's inequality and its applications[J]. AIMS Mathematics, 2025, 10(11): 26058-26076. doi: 10.3934/math.20251147

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Abstract

The aim of this article is to introduce a novel and logically motivated approach that successfully yields a new refinement of the discrete form of Jensen's inequality. The proposed refinement is further applied to several important areas, including inequalities involving means, Hölder's inequality, and information theory, thereby demonstrating both the theoretical strength and practical utility of the result.

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