Sándor-Yang平均关于经典平均凸组合的确界

doi:10.3785/j.issn.1008-9497.2018.06.004

摘要
图/表
参考文献
相关文章 (15)

全文: PDF (1004 KB) HTML( )
输出: BibTeX | EndNote (RIS)

摘要应用实分析方法，研究Sándor-Yang平均R_GQ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R_QG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R_GQ和R_QG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.

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	张帆
	杨月英
	钱伟茂

关键词 ： Sá, ndor-Yang平均, 经典平均, 不等式

Abstract：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.

Key words： Sándor-Yang mean classical mean inequality

收稿日期: 2018-02-28

ZTFLH:

O174.6

基金资助: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）.

通讯作者: 杨月英,ORCID:http://orcid.org/0000-0003-3644-460X,E-mail:yyy1008hz@163.com. E-mail: yyy1008hz@163.com

作者简介: 张帆(1977-),ORCID:http://orcid.org/0000-0003-0689-946X,男,硕士,讲师,主要从事解析不等式研究.

引用本文:

张帆, 杨月英, 钱伟茂. Sándor-Yang平均关于经典平均凸组合的确界[J]. 浙江大学学报（理学版）, 2018, 45(6): 665-672.
ZHANG Fan, YANG Yueying, QIAN Weimao. Sharp bounds for Sándor-Yang means in terms of the convex combination of classical bivariate means. Journal of ZheJIang University(Science Edition), 2018, 45(6): 665-672.

链接本文:

http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.06.004 或 http://www.zjujournals.com/sci/CN/Y2018/V45/I6/665

[1] YANG Z H. Three families of two-parameter means constructed by trigonometric functions[J].Journal of Inequalites and Application, 2013:541.
[2] NEUMAN E, SÁNDOR J. On the Schwab-Borchardt mean[J]. Math Pannon, 2003, 14(2):253-266.
[3] NEUMAN E, SÁNDOR J. On the Schwab-Borchardt meanⅡ[J]. Math Pannon, 2006, 17(1):49-59.
[4] SEIFFERT H J. Aufgabeβ16[J]. Die Wurzel, 1995(29):221-222.
[5] LI J F, YANG Z H, CHU Y M. Optimal power mean bounds for the second Yang mean[J]. Journal of Inequalites and Application, 2016(31):1-9.
[6] QIAN W M, CHU Y M. Best possible bounds for Yang mean using generalized logarithmic mean[J]. Mathematical Problems in Engineering, 2016(2):1-7.
[7] QIAN W M, CHU Y M, ZHANG X H. Sharp one-parameter mean bounds for Yang mean[J]. Mathematical Problems in Engineering, 2016(1):1-5.
[8] BULLEN P S, MITRINOVIC' D S, VASIC' P MP. Means and Their Inequalities[M]. Dordrecht:Springer, 1988.
[9] NEUMAN E. On a new family of bivariate means[J]. Journal of Inequalites and Application, 2017, 11(3):673-681.
[10] YANG Z H,CHU Y M. Optimal evaluations for the Sándor-Yang mean by power mean[J]. Mathematical Inequalities & Applications, 2016,19(3):1031-1038.
[11] ZHAO T H, QIAN W M, SONG Y Q. Optimal bounds for two Sándor-type means in terms of power means[J] Journal of Inequalites and Application, 2016(1):1-10.
[12] YANG Y Y, QIAN W M. Two optimal inequalities related to the Sándor-Yang type mean and one-parameter mean[J]. Communications in Mathematical Research, 2016,32(4):352-358.
[13] 徐会作. Sándor-Yang平均关于一些二元平均凸组合的确界[J]. 华东师范大学学报(自然科学版), 2017(4):41-51. XU H Z. Sharp bounds for Sándor-Yang means in terms of some bivariate means[J]. Journal of East China Normal University (Natural Science), 2017(4):41-51.
[14] WANG J L, XU H Z, QIAN W M. Sharp bounds for Sándor-Yang means in terms of Lehmer means[J]. Recent Advances in Inequalities and Applications, 2018(2):1-8.