New Inequalities for Means - Arslanagić, Š.; Bencze, M. (Sarajevo Journal of Mathematics, 2024)
In this paper we present new inequalities for means. If $$ 0<a<b, \;A(a,b)=\frac{a+b}{2},\; G(a,b)=\sqrt{ab},\; H(a,b)=\frac{2ab}{a+b}, $$ $$ L(a,b)=\frac{b-a}{\ln{b}-lna},\; I(a,b)=\frac{1}{e}\left(\frac{b^b}{a^a}\right)^{\frac{1}{b-a}}, $$ we will prove seven new theorems concerning these means. 2000 Mathematics Subject Classification. 26A48, 26D20