A Refined form of the generalized Jensen inequality through an arbitrary function

Volume 39, Issue 3, pp 376--385 https://dx.doi.org/10.22436/jmcs.039.03.06

Publication Date: April 15, 2025 Submission Date: February 22, 2025 Revision Date: March 10, 2025 Accteptance Date: March 22, 2025

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Authors

S. Sahar - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. M. A. Khan - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. Sh. Khan - Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. S. H. Altoum - Department of Mathematics, University College of Qunfudhah, Umm Al-Qura University, Makkah, Saudi Arabia. E. R. Nwaeze - Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA.

Abstract

This article is about a refined form of the generalized Jensen inequality in Riemann sense, which is obtained through a positive integrable function. Then manipulation of certain functions with suitable substitutions in the proposed result enables to establish new refined inequalities for the well-known Hölder, and celebrated Hermite--Hadamard inequalities along with power, and quasi-arithmetic means. Further the proposed result also gives refined estimates to Csiszár divergence and its particular variants.

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Keywords

• Jensen inequality
• Hermite--Hadamard inequality
• Hölder inequality
• Csiszár divergence

MSC

•  26A33
•  26A51
•  26D15

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