Applications of Weighted Arithmetic-Geometric Means Inequality to Functional Inequalities

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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