Some estimates on the AM-GM inequality and its applications

Subject Areas : Functional analysis

F. P. Mohebbi ¹ , M. Hassani ² , M. Erfanian Omidvar ³ , H. Moradi ⁴

1 - Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran
2 - Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran
3 - Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran
4 - Department of Mathematics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran

Received: 2024-03-01 Accepted : 2024-05-12 Published : 2024-05-15

Keywords: Young inequality, arithmetic-geometric mean inequality, logarithmic mean,

Abstract :

‎The present paper seeks to establish an approximation of the arithmetic-geometric mean inequality (AM-GM) using a logarithmically concave function‎. ‎We utilized the specific properties of this class of functions to derive modified versions of the AM-GM inequality as a specific example‎. ‎These findings present a fresh perspective on the subject‎.

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