Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means. (12th August 2010) - Chu, Yu-Ming; Qiu, Ye-Fang; Wang, Miao-Kun
Abstract : We answer the question: forα ∈ ( 0, 1 ), what are the greatest valuep and the least valueq such that the double inequalityM p ( a, b ) < P α ( a, b ) G 1 − α ( a, b ) < M q ( a, b ) holds for alla, b > 0 witha ≠ b . Here, M p ( a, b ), P ( a, b ), andG ( a, b ) denote the power of orderp, Seiffert, and geometric means of two positive numbersa andb, respectively.