两个涉及Seiffert和Neuman平均的双向不等式  

Two the Double Inequalities Involving Seiffert and Neuman Means

作　　者：沈林昌 王君丽[2] SHEN Lin-chang;WANG Jun-li(Huzhou Shanlian Adult School, Huzhou 313000, China;School of Adult Education, Taizhou Vocational College of Science & Technology, Taizhou 318020, China)

机构地区：[1]湖州善琏成人文化学校,浙江湖州313000 [2]台州科技职业学院成人教育学院,浙江台州318020

出　　处：《湖州职业技术学院学报》2017年第3期74-77,共4页Journal of Huzhou Vocational and Technological College

摘　　要：应用实分析的方法,找到了最佳参数α_1,α_2,β_1,β_2∈(0,1)使得双向不等式:A^(α1)(a,b)X^(1-α1)(a,b)<P(a,b)<A^(β1)(a,b)X^(1-β1)(a,b),A^(α2)(a,b)X^(1-α2)(a,b)<N_(GA)(a,b)<A^(β2)(a,b)X^(1-β2)(a,b)对所有a,b>0和a≠b成立。其中P(a,b),N_(GA)(a,b),X(a,b)和A(a,b)分别表示两个正数a和b的第一类Seiffert平均,Neuman平均,Sándor平均和算术平均。In this paper,we apply the method of real analysisand and find the best possible parameterα1,α2,β1,β2∈(0,1)such that the double inequalities:Aα1(a,b)X1-α1(a,b)<P(a,b)<Aβ1(a,b)X1-β1(a,b),Aα2(a,b)X1-α2(a,b)<NGA(a,b)<Aβ2(a,b)X1-β2(a,b)hold for all a,b>0and a≠b,where P(a,b),NGA(a,b),X(a,b)and A(a,b)are the fires Seiffert,Neuman,Sándor and arithmetic means of two positive numbers a and b,respectively.

关 键 词：第一类Seiffert平均 Neuman平均 Sándor平均 算术平均 不等式 

分 类 号：O151.23[理学—数学]