SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 797-806.

SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

褚玉明|赵铁洪|宋迎清

School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China； Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China； School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China

收稿日期:2013-03-23 修回日期:2013-08-29 出版日期:2014-05-20 发布日期:2014-05-20
基金资助:
This research was supported by the Natural Science Foundation of China under Grants 61374086 and 11371125, and the Natural Science Foundation of Zhejiang Province under Grant LY13A010004.

SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

CHU Yu-Ming, ZHAO Tie-Hong, SONG Ying-Qing

School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China； Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China； School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China

Received:2013-03-23 Revised:2013-08-29 Online:2014-05-20 Published:2014-05-20
Supported by:
This research was supported by the Natural Science Foundation of China under Grants 61374086 and 11371125, and the Natural Science Foundation of Zhejiang Province under Grant LY13A010004.

摘要/Abstract

摘要：

In this article, we prove that the double inequality
αP(a, b) + (1 − α)Q(a, b) < M(a, b) < βP(a, b) + (1 − β)Q(a, b)
holds for any a, b > 0 with a ≠b if and only if α ≥ 1/2 and β ≤ [π(√2 log(1 + √2) −1)]/[(√2π−2) log(1+√2)] = 0.3595 · · · , where M(a, b), Q(a, b), and P(a, b) are the Neuman-S´andor, quadratic, and first Seiffert means of a and b, respectively.

关键词: Neuman-S´andor mean, quadratic mean, first Seiffert mean

Abstract:

Key words: Neuman-S´andor mean, quadratic mean, first Seiffert mean

中图分类号:

26E60

褚玉明, 赵铁洪, 宋迎清. SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS[J]. 数学物理学报, 2014, 34(3): 797-806.

CHU Yu-Ming, ZHAO Tie-Hong, SONG Ying-Qing. SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS[J]. Acta mathematica scientia,Series A, 2014, 34(3): 797-806.

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SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

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