Applications of Weighted Arithmetic-Geometric Means Inequality to Functional Inequalities

Authors : Halil İbrahim ÇELİK

Pages : 27-31

Doi:10.30931/jetas.303624

View : 15 | Download : 10

Publication Date : 2017-04-30

Article Type : Research Paper

Abstract :In this paper we  prove  the functional  inequality $finsert ignore into journalissuearticles values(x);^{finsert ignore into journalissuearticles values(x);}\leq ginsert ignore into journalissuearticles values(x);^{ginsert ignore into journalissuearticles values(x);}$ 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