In this paper,the order relations of Toader type mean with respect to the convex combination of harmonic and Neuman means are studied.By using the monotonicity L'Hospital rule,sharp bounds of con-vex combination of harmonic and Neuman means for Toader type mean are proved.As applications,two inequalities for the inverse hyperbolic sine and inverse tangent function for the second kind of complete el-liptic integral are given,respectively.The results are an improvement on some known results.
关键词
完全椭圆积分/TOADER平均/NEUMAN平均/调和平均
Key words
complete elliptic integral/Toader mean/Neuman mean/harmonic mean
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