双纽线平均的算术和形心平均的确界  

Sharp Bounds for the Lemniscatic Mean in Terms of Arithmetic and Centroidal Means

作　　者：张帆[1] 钱伟茂[2] 徐会作 ZHANG Fan;QIAN Wei-mao;XU Hui-zuo(School of Civil Engineering,Huzhou Vocational&Technical College,Huzhou 313000,China;School of Continuing Education,Huzhou Vocational Sz Technical College,Huzhou 313000,China;School of Mathematics and Information Engineering,Wenzhou Institute of Technology,Wenzhou 325000,China)

机构地区：[1]湖州职业技术学院建筑工程学院,浙江湖州313000 [2]湖州职业技术学院继续教育学院,浙江湖州313000 [3]温州理工学院数学与信息工程学院,浙江温州325000

出　　处：《数学的实践与认识》2021年第18期293-304,共12页Mathematics in Practice and Theory

基　　金：浙江省自然科学基金资助项目(LY13 A010004);2020年浙江省教育厅一般科研项目(Y202043179)。

摘　　要：应用实分析方法,研究了两个双纽线平均关于算术平均和形心平均调和组合(或凸组合)之间的序关系,得到这两个双纽线平均关于算术平均和形心平均调和组合(或凸组合)的确界.作为应用,分别给出了反双纽线双曲正弦函数和反双纽线正切函数的不等式链,所得结果是对一些已知结果的改进.By using the method of real analysis,the order relations between the lemniscatic means and harmonic combination(or convex combination) of arithmetic and centroidal means are studied in this paper,the sharp bounds for lemniscatic means with respect to harmonic combination(or convex combination) of arithmetic and centroidal means are obtained.As an application,the inequality chains of hyperbolic arc lemniscate sine function and hyperbolic arc lemniscate tangent function are given respectively.The obtained results are the improvement of some known results.

关 键 词：反双纽线函数 双纽线平均 算术平均 形心平均 不等式 

分 类 号：O174[理学—数学]