【摘要】 利用函数的同序和反序概念，研究了函数幂加权平均值的性质及其关于其幂指数的函数特性（如对数凸性及单调性）．作为应用，引进了一个新的平均值，比较了Holder平均值和Stolarsky平均值．同时得到Ostle－Terwilliger不等式及算术-几何不等式的加细的结果．更多还原

【Abstract】 By means of the concepts of the same order and the oppoite order between functions, studiedthe properties of weighted powr means of functions and their functional characteristics such as the loga-rithmic convexity and monotony when they are considered as functions of their power exponents. As appli-cations a new mean was introduced, comparisons between the so-called Holder’s means and the Sto-larsky’s means were made, and results of the refinements of the Ostle-Tewlliger inequality and of thearithmtic-geometric mean inequality were obtained.更多还原