Toader-Qi平均关于对数和算术平均特殊组合的确界  

The Exact Boundary of Toader-Qi Mean on Special Combination of Logarithmic and Arithmetic Mean

作　　者：王君丽[1] 徐会作[2] 钱伟茂[3] WANG Junli;XU Huizuo;QIAN Weimao(School of Adult Education,Taizhou Vocational College of Science&Technology,Taizhou,Zhejiang 318020;Teacher Development Center,Wenzhou Broadcast and TV University,Wenzhou,Zhejiang 325000;School of Continuing Education,Huzhou Broadcast and TV University,Huzhou,Zhejiang 313000)

机构地区：[1]台州科技职业学院成人教育学院,浙江台州318020 [2]温州广播电视大学教师教学发展中心,浙江温州325000 [3]湖州广播电视大学继续教育学院,浙江湖州313000

出　　处：《绍兴文理学院学报》2020年第8期48-56,共9页Journal of Shaoxing University

基　　金：浙江省自然科学基金项目“拟双曲度量和共形映射的稳定性理论研究”(LY13A010004);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);浙江广播电视大学人才培养项目“312人才培养工程”(NO.7).

摘　　要：研究了Toader-Qi平均TQ(a,b)关于对数平均L(a,b)和算术平均A(a,b)特殊组合的序关系.运用第1类修正Bessel函数的Cauchy乘积公式,建立若干重要引理,给出了3个有关Toader-Qi平均TQ(a,b)的精确不等式,并且推得了第1类修正Bessel函数I0(t)新的确界.The order relations of some special combinations of logarithmic mean L(a,b)and arithmetic mean A(a,b)for the Toader-Qi mean TQ(a,b)were studied.By using the Cauchy product formula of Class 1 modified Bessel function,some important lemmas are established,three exact inequalities about the Toader-Qi mean are given,and the new definite boundaries of Class 1 modified Bessel function I 0(t)are derived.

关 键 词：Toader-Qi平均 第1类修正贝塞尔函数 对数平均 算术平均 不等式 

分 类 号：O174.6[理学—数学]