一个特殊拟算术平均的两个精确不等式  

Two Sharp Inequalities for a Special Quasi arithmetic Mean

作　　者：钱伟茂[1] QIAN Wei-mao(School of Continuing Education,Huzhou Vocational and Technological College,Huzhou 313000,China)

机构地区：[1]湖州职业技术学院继续教育学院,浙江湖州313000

出　　处：《湖州职业技术学院学报》2020年第3期51-54,共4页Journal of Huzhou Vocational and Technological College

基　　金：2019年度浙江广播电视大学科学研究课题“两类对称积分及其衍生平均的研究”(XKT-19Z02)的研究成果之一。

摘　　要：运用实分析方法,研究一个特殊拟算术平均与几何、算术及反调和平均组合的序关系,得到了特殊拟算术平均关于几何、算术及反调和平均的两个精确不等式.作为应用,给出了第二类完全椭圆积分两个新的确界.获得的结果是对已有相关结果的改进和推广.This paper studies the combination of the geometric,arithmetic and contra harmonic means for the special quasi arithmetic mean by using the real analysis method.The main results obtained are two sharp inequalities for the quasi arithmetic mean in terms of the geometric,arithmetic and contra harmonic means.Two new definite bounds for complete elliptic integrals of the second kind are derived as applications.The results are the improvement and promotion of the previously known results.

关 键 词：拟算术平均 完全椭圆积分 算术平均 几何平均 反调和平均 

分 类 号：O172[理学—数学]