Neuman平均的算术与二次平均的最佳凸组合界

Optimal Convex Combination Bounds of Arithmetic and Quadratic Means for Neuman Mean

运用初等微积分知识,研究了Neuman平均N QG、算术平均A与二次平均Q的凸组合关系,证得了Neuman平均N QG关于算术平均A与二次平均Q凸组合的确界.作为应用,给出了一个第一类Yang平均U关于几何平均G、算术平均A和二次平均Q的不等式,并推出了反正切函数的一个新确界.

Using the elementary calculus knowledge,the article studies the Neuman mean N QG with respect to the convex combinations of the arithmetic mean A and quadratic mean Q,and obtains the definite bounds of Neuman mean N QG about arithmetic mean A and quadratic mean Q.As an application,it gives an inequality for the first Yang mean U with respect to the geometric mean G,the arithmetic mean A and the quadratic mean Q,and derives a new definite bound for the inverse tangent function.