算术与Toader平均凸组合的单参数平均确界

Bounds for Convex Combination of Arithmetic and Toader Means in Terms of One parameter Means

运用实分析方法,研究算术和Toader平均凸组合关于单参数心形(或二次)平均的确界,得到了两个精确双向不等式.研究方法和结果对平均值理论的相关研究具有一定的启示作用.

Using the method of real analysis,the article studies the sharp bounds for convex combination of the arithmetic and Toader means in terms of one parameter centroidal or quadratic means.Two sharp mutual direction inequalities are obtained.The research methods and results can enlighten the related researches on mean value theory.