Toader-Qi平均与其他二元平均的几个确界

摘要

This paper study the order relation of some special combinations of geometric mean G(a,b), logarithmic mean L(a,b), arithmetic mean A(a,b) and quadratic mean Q(a,b) for Toader-Qi mean TQ(a,b).By using the method of real analysis in mathematics and the product formula of the first kind Bessel function, several important lemma are established, and four optimal inequalities for Toader-Qi mean TQ(a,b) are found.The results of particular cases are also presented.%研究了Toader-Qi平均TQ(a,b)关于几何平均G(a,b)、对数平均L(a,b)、算术平均A(a,b)和二次平均Q(a,b)若干特殊组合的序关系.运用实分析方法以及第1类Bessel函数的乘积公式,建立若干重要引理,导出了4个关于Toader-Qi平均TQ(a,b)的精确不等式,并获得了特殊情形的结果.