%0 Journal Article
%T Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Chu, Y.
%A Hou, S.
%A Xia, W.
%D 2013
%\ 05/15/2013
%V 39
%N 2
%P 259-269
%! Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
%K logarithmic mean
%K identric mean
%K centroidal mean
%K harmonic mean
%R
%X We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)0$ with $aneq b$. Here, $C(a,b)$, $H(a,b)$, $L(a,b)$, and $I(a,b)$ are the centroidal, harmonic, logarithmic, and identric means of two positive numbers $a$ and $b$, respectively.
%U http://bims.iranjournals.ir/article_411_ce7ebf9563324f84f8dface04487e196.pdf