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Research Article | Open Access

Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions

Asadullah Sohail1, Muhammad Adil Khan1, Xiaoye Ding2( ), Mohamed Sharaf3, Mohammed A. El-Meligy4,5
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
General Education Department, Anhui Xinhua University, Hefei 230088, China
Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
Applied Science Research Center, Applied Science Private University, Amman, Jordan
Jadara University Research Center, Jadara University, P.O. Box 733, Irbid, Jordan
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Abstract

Jensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the absolute sense. We conducted numerical experiments to compare our primary results with previously established findings. Additionally, we provided several applications of our major results to classical inequalities, means, and divergences.

Keywords

convex functionconcave functionJensen's inequalityHölder inequality
CLC number: 26A42, 26A51, 26D15

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 33973-33994
DOI: 10.3934/math.20241620

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Cite this article:
Sohail A, Khan MA, Ding X, et al. Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions. AIMS Mathematics, 2024, 9(12): 33973-33994. https://doi.org/10.3934/math.20241620

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Received: 14 September 2024
Revised: 11 November 2024
Accepted: 20 November 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)