Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means

被引：0
|
作者：
He, Zai-Yin [1 ]
Jiang, Yue-Ping [1 ]
Chug, Yu-Ming [2 ]
机构：
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
[2] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS | 2019年 / 10卷 / 03期
关键词：
Toader mean; Second Seiffert mean; Arithmetic mean; COMPLETE ELLIPTIC INTEGRALS; RAMANUJANS CUBIC TRANSFORMATION; SHARP INEQUALITIES; RESPECT; CONCAVITY; KIND;
D O I：
10.26713/cma.v10i3.1200
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the article, we prove that the double inequalities alpha T-1(a, b) + (1 - alpha(1))A(a, b) < TD(a, b) < beta T-1(a, b) + (1 - beta(1))A(a, b), T-alpha 2(a, b)A(1-alpha 2)(a, b) < TD(a, b) < (T-beta 2(a, b)A(1-)(beta 2)(a, b) hold for all a, b > 0 with a not equal b if and only if alpha(1) <= 3/4, beta(1) >= 1, alpha(2 )<= 3/4 and beta(2) >= 1 where A(a,b), TD(a, b) and T(a, b) are the arithmetic, Toader and second Seiffert means of a and b, respectively.
引用
收藏
页码：561 / 570
页数：10
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