An Optimal Double Inequality between Seiffert and Geometric Means. (23rd November 2011) - Chu, Yu-Ming; Wang, Miao-Kun; Wang, Zi-Kui
Abstract : Forα, β ∈ ( 0, 1 / 2 ) we prove that the double inequalityG ( α a + ( 1 − α ) b, α b + ( 1 − α ) a ) < P ( a, b ) < G ( β a + ( 1 − β ) b, β b + ( 1 − β ) a ) holds for alla, b > 0 witha ≠ b if and only ifα ≤ ( 1 − 1 − 4 / π 2 ) / 2 andβ ≥ ( 3 − 3 ) / 6 . Here, G ( a, b ) andP ( a, b ) denote the geometric and Seiffert means of two positive numbersa andb, respectively.