Sándor-Yang平均关于经典平均凸组合的确界  

Sharp bounds for Sándor-Yang means in terms of the convex combination of classical bivariate means

作　　者：张帆[1] 杨月英[2] 钱伟茂[3] ZHANG Fan;YANG Yueying;QIAN Weimao(School of Architecture Engineering,Huzhou Vocational&Technical College,Huzhou 313000,Zhejiang Province,China;Mechanic Electronic and Automobile Egineering College,Huzhou Vocational&Technical College,Huzhou 313000,Zhejiang Province,China;School of Distance Education,Huzhou Broadcast and TV University,Huzhou 313000,Zhejiang Province,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]湖州职业技术学院机电与汽车工程学院,浙江湖州313000 [3]湖州广播电视大学远程教育学院,浙江湖州313000

出　　处：《浙江大学学报（理学版）》2018年第6期665-672,共8页Journal of Zhejiang University（Science Edition）

基　　金：浙江省自然科学基金资助项目(LY13A010004);浙江广播电视大学科学研究课题(XKT-17G26);湖州职业技术学院校教改课题(2016xj26)

摘　　要：应用实分析方法,研究Sándor-Yang平均RGQ关于算术平均A与几何平均G(或调和平均H)凸组合和Sándor-Yang平均RQG与算术平均A与二次平均Q(或反调和平均C)凸组合的序关系,以及两Sándor-Yang平均RGQ和RQG与几何平均G、算术平均A、二次平均Q的序关系,得到了4个精确双向不等式和一个新的不等式链.This article presents several sharp bounds for the Sándor-Yang mean R GQ in terms of the convex combination of arithmetic mean A and geometric mean G(arithmetic mean A and harmonic mean H),the Sándor-Yang mean R QG in terms of the convex combination of quadratic mean Q and arithmetic mean A(contra-harmonic mean C and arithmetic mean A).A new chain of inequalities for the geometric mean G,arithmetic mean A,quadratic mean Q and two Sándor-Yang means R GQ and R QG are then derived.

关 键 词：Sándor-Yang平均 经典平均 不等式 

分 类 号：O174.6[理学—数学]