Applications of Weighted Arithmetic-Geometric Means Inequality to Functional Inequalities

Year 2017, , 27 - 31, 30.04.2017

Halil İbrahim Çelik

https://doi.org/10.30931/jetas.303624

Abstract

In this paper we  prove  the functional  inequality $f(x)^{f(x)}\leq g(x)^{g(x)}$ for positive real functions $f$ and $g$ satisfying natural conditions and apply it to derive
inequalities  between some of the elementary functions and to prove monotonocity of certain sequences of real numbers.

Keywords

Arithmetic-geometric means inequality, Young inequality, Extremum values, Functional inequalities, Elementary functions, Monotone sequences

References

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• [4] Thomas.J. Mildford, Olympiad Inequalites, 2006, http://www.unl.edu/amc.
• [5] W. Rudin, Real and Complex Analysis , McGraw-Hill Book Company, New York, 1987.