A Refined Jensen Inequality Connected to an Arbitrary Positive Finite Sequence

Shanhe Wu (), Muhammad Adil Khan, Tareq Saeed and Zaid Mohammed Mohammed Mahdi Sayed
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Shanhe Wu: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Muhammad Adil Khan: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Tareq Saeed: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Zaid Mohammed Mohammed Mahdi Sayed: Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

Mathematics, 2022, vol. 10, issue 24, 1-10

Abstract: The prime purpose of this paper is to provide a refinement of Jensen’s inequality in connection with a positive finite sequence. We deal with the refinement for particular cases and point out the relation between the new result with earlier results of Jensen’s inequality. As results, we obtain refinements of the quasi-arithmetic and power mean inequalities. Finally, several results are obtained in information theory with the help of the main results.

Keywords: Jensen’s inequality; power means; Hölder inequality; information theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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