New Inequalities for Means
DOI:
https://doi.org/10.5644/SJM.04.1.04Keywords:
Arithmetic, geometric, harmonic and logarithmic mean, inequalities between means, convex and concave function, power-mean and Hadamard’s inequalityAbstract
In this paper we present new inequalities for means. If $$ 0<a<b,
\;A(a,b)=\frac{a+b}{2},\; G(a,b)=\sqrt{ab},\;
H(a,b)=\frac{2ab}{a+b}, $$ $$ L(a,b)=\frac{b-a}{\ln{b}-ln{a}},\;
I(a,b)=\frac{1}{e}\left(\frac{b^b}{a^a}\right)^{\frac{1}{b-a}},
$$ we will prove seven new theorems concerning these means.
2000 Mathematics Subject Classification. 26A48, 26D20
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References
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