Proof without words: Two inequalities proved by convexity

摘要

The purpose of this note is to prove, almost without words, the following inequalities:(1) ifα>1,and0<ω<1,then(1+ω)~α-1/(1+ω)~α-ω~α>ω(2) if0<α<1,and0<ω<1,then(1+ω)~ α-1/(1+ω)~α<ω.