SHARP BOUNDS FOR TOADER-TYPE MEANS IN TERMS OF TWO-PARAMETER MEANS

作     者：Yueying YANG Weimao QIAN Hongwei ZHANG Yuming CHU 杨月英;钱伟茂;张宏伟;褚玉明

作者机构：School of Mechanical and Electrical EngineeringHuzhou Vocational&Technical CollegeHuzhou 313000China School of Continuing EducationHuzhou Vocational&Technical CollegeHuzhou 313000China School of Mathematics and StatisticsChangsha University of Science&TechnologyChangsha 410014China Department of MathematicsHuzhou UniversityHuzhou 313000China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2021年第41卷第3期

页      面：719-728页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Natural Science Foundation of China(61673169 11301127 11701176 11626101 11601485) 

主　　题：Geometric mean arithmetic mean Toader mean ontraharmonic mean complete elliptic integral 

摘      要：In the article,we prove that the double inequalities Gp[λ1a+(1-λ1)b,λ1 b+(1-λ1)a]A1-p(a,b)0 with a≠b if and only ifλ1≤1/2-(1-(2/π)2/p)1/2/2,μ1≥1/2-(2p)1/2/(4 p),λ2≤1/2+(2(3/(2 s)(E(21/2/2)/π)1/s)-1)1/2/2 andμ2≥1/2+s1/2/(4 s)ifλ1,μ1∈(0,1/2),λ2,μ2∈(1/2,1),p≥1 and s≥1/2,where G(a,b)=(ab)1/2,A(a,b)=(a+b)/2,T(a,b)=∫0π/2(a2 cos2 t+b2 sin2)1/2 tdt/π,Q(a,b)=((a2+b2)/2)1/2,C(a,b)=(a2+b2)/(a+b)and E(r)=∫0π/2(1-r^(2) sin^(2))1/2 tdt.