特殊拟算术型平均与算术、调和平均的最佳不等式  

Optimal Inequalities for Special Quasi-Arithmetic Type Mean in Terms of Arithmetic and Harmonic Means

作　　者：徐仁旭 徐会作 钱伟茂[3] XU Renxu;XU Huizuo;QIAN Weimao(Office of Academic Affairs,Zhejiang College of Construction,Hangzhou 311231,China;School of Mathematics and Information Engineering,Wenzhou University of Technology,Wenzhou 325000,China;School of Distance Education,Huzhou Broadcast and TV University,Huzhou 313000,China)

机构地区：[1]浙江建设职业技术学院教务处,浙江杭州311231 [2]温州理工学院数学与信息工程学院,浙江温州325000 [3]湖州广播电视大学远程教育学院,浙江湖州313000

出　　处：《东莞理工学院学报》2022年第5期7-12,共6页Journal of Dongguan University of Technology

基　　金：浙江省自然科学基金项目(LY13A010004);浙江省属高校基本科研业务费项目(Z202007);浙江省高等教育学会2020年度高等教育研究课题(KT2020244)。

摘　　要：应用实分析的方法,研究了一个特殊拟算术平均关于算术、调和平均的组合以及单参数调和平均的序关系,证得了三个精确不等式,作为应用给出了第二类完全椭圆积椭分三个新的上下界,获得结果是对已有相关结果的改进和推广。This paper studies the combination of arithmetic,harmonic and one-parameter harmonic means for the special quasi-arithmetic mean by using the real analysis method.The main results obtained are three sharp inequalities.Three new definite bounds for complete elliptic integrals of the second kind are derived as applications.The results are the improvement and promotions of the previously known results.

关 键 词：拟算术平均 完全椭圆积分 算术平均 调和平均 单参数调和平均 

分 类 号：O174.6[理学—数学]