A log-convex approach to Jensen-Mercer inequality

Subject Areas : Functional analysis

M. Davarpanah ¹ , H. R. Moradi ²

1 - Department of Mathematics, Ferdows Branch, Islamic Azad University, Ferdows, Iran
2 - Department of Mathematics, Payame Noor University (PNU), P.O. Box, 19395-4697, Tehran, Iran

Received: 2022-07-25 Accepted : 2022-09-15 Published : 2022-09-01

Keywords: Inequality, Hermite-Hadamard inequality, Jensen-Mercer, Fejer inequality, log-convex function,

Abstract :

‎We obtain some new Jensen-Mercer type inequalities for log-convex functions‎. ‎Indeed‎, ‎we establish refinement and reverse for the Jensen-Mercer inequality for log-convex functions‎. ‎Several new Hermite-Hadamard and Fej\'er types of inequalities are also presented‎.‎

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