... −1πH a, b,2.24for all a, b > 0witha/ b.2 Journal of Inequalities and ApplicationsLet C a, b a 2b2/ a b ,A a, b a b/2,G a, b√ab,andH a, b2ab/ a b be the contraharmonic, ... Neuman and J. S´andor, On certain means of two arguments and their extensions,” InternationalJournal of Mathematics and Mathematical Sciences, no. 16, pp. 981–993, 2003.Journal of Inequalities ... means,” Journal of Inequalities and Applications, vol. 2006, Article ID 46782, 25 pages, 2006.21 T. Hara, M. Uchiyama, and S E. Ta kahasi, “ A refinement of various mean inequalities, ” Journal...