经典平均在物理学和力学中有广泛的应用,它们之间的估计式是近年来的热门研究对象.本文考虑第1类反调和平均、对数平均和幂平均之间的估计式,建立了第1类反调和平均和对数平均关于幂平均的最优凸组合界.这些结果是经典结论的推广和发展.
[1] 王挽澜, 文家金, 石焕南. 幂平均不等式的最优值 [J]. 数学学报 2004.doi:10.3321/j.issn:0583-1431.2004.06.002
[2] LONG Boyong, CHU Yuming. Optimal power mean bounds for the weighted geometric mean of classical means [J]. Journal of Inequalities and Applications 2010, ID 905679.
[3] XIA Weifeng, CHU Yuming, WANG Gendi. The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means [J]. Abstract and Applied Analysis 2010, ID 604804.
[4] CHU Yuming, XIA Weifeng. Two sharp inequalities for power mean, geometric mean and harmonic mean [J]. Journal of Inequalities and Applications 2009, ID 741923.
[5] Wu SH. Generalization and sharpness of the power means inequality and their applications [J]. Journal of Mathematical Analysis and Applications 2005, 2(2).
[6] Richards KC. Sharp power mean bounds for the Gaussian hypergeometric function [J]. Journal of Mathematical Analysis and Applications 2005, 1(1).
[7] HAASTO P A. Optimal inequalities between Seiffert's mean and power mean [J]. Mathematical Inequalities and Applications 2004, 7(01).
[8] TARNAVAS C D, TARNAVAS D D. An inequality for mixed power means [J]. Mathematical Inequality and Applications 1999, 2(02).
[9] BUKOR J, TOTH J, ZSILINSZKY L. The logarithinic mean and the power mean of positive numbers [J]. Octogon Mathematical Magazine 1994, 2(01).
[10] PECARIC J E. Generalization of the power means and their inequalities [J]. Journal of Mathematical Analysis and Applications 1991, 161(02).
[11] CHEN Ji, HU Bo. The identric mean and the power mean inequalities of Ky Fan type [J]. Facta Universitatis 1989, 4.
[12] ALZER H, JANOUS W. Solution of problem 8 [J]. Crux Mathematicorum 1987, 13.
[13] BULLEN P S, MRITRINOVIC D S, VASIC P M. Means and their inequalities [J]. Mathematics and Its Applications:East European eries 1998, 31.
[14] MAO Qiji. Power mean, logarithmic mean and Heronian dual mean of two positive numbers [J]. Journalof Suzhou College of Education 1999, 16(1-2).
[15] CARLSON B C. The logarithmic mean [J]. American Mathematical Monthly 1972, 79.
[16] LEACH E B, SHOLANDER M C. Extended mean values Ⅱ [J]. Journal of Mathematical Analysis and Applications 1983, 92(01).
[17] SANDOR J. A note on some inequalities for means [J]. Archivder Mathematik 1991, 56(05).
[18] SHI Mingyu, CHU Yuming, JIANG Yueping. Optimal Inequalities among various means of two arguments [J]. Abstract and Applied Analysis 2009, ID 694394.
