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本刊87年第3期30页用“组合知识”证明了一组条件不等式。这些结果,在函数的凹凸性质看来是显然的,而限于初等方法却颇具技巧。本文将应用平均值不等式和连乘的技巧证明几个更一般性的命题,其方法本身为这类不等式提供了一个较为经济而统一的处理。
The 30th issue of the 3rd issue of the Journal of the People’s Republic of China (1987) used “combined knowledge” to prove a set of conditional inequalities. These results appear to be apparent in the bumpy nature of the function, but are limited by the elementary method. This article will use the mean inequality and the multiplication technique to prove several more general propositions. The method itself provides a more economical and unified treatment for such inequalities.