Sharp bounds for Sándor-Yang means in terms of single parameter harmonic and contra-harmonic means

LI Shaoyun; QIAN Weimao; XU Huizuo

doi:10.3969/j.issn.1000-5641.201911015

Issue 4

Jul. 2020

Turn off MathJax

Article Contents

Article Navigation > Journal of East China Normal University (Natural Sciences) > 2020 > (4): 26-34

LI Shaoyun, QIAN Weimao, XU Huizuo. Sharp bounds for Sándor-Yang means in terms of single parameter harmonic and contra-harmonic means[J]. Journal of East China Normal University (Natural Sciences), 2020, (4): 26-34. doi: 10.3969/j.issn.1000-5641.201911015

Citation:

LI Shaoyun, QIAN Weimao, XU Huizuo. Sharp bounds for Sándor-Yang means in terms of single parameter harmonic and contra-harmonic means[J]. Journal of East China Normal University (Natural Sciences), 2020, (4): 26-34. doi: 10.3969/j.issn.1000-5641.201911015

Citation:

PDF( 573 KB)

Sharp bounds for Sándor-Yang means in terms of single parameter harmonic and contra-harmonic means

doi: 10.3969/j.issn.1000-5641.201911015

LI Shaoyun^1
,,
QIAN Weimao^{2
,
,},
XU Huizuo¹

1.
Teacher’s Teaching Development Center, Wenzhou Broadcast and TV University, Wenzhou, Zhejiang　325013, China
2.
School of Continuing Education, Huzhou Broadcast and TV University, Huzhou, Zhejiang　313000, China

Received Date: 2019-03-18
Available Online: 2020-07-20
Publish Date: 2020-07-25

Abstract

Abstract

Using real analysis, this paper reviews the order relations of Sándor-Yang means and single parameter harmonic (or contra-harmonic) means. Two optimal double inequalities are found.
- Sándor-Yang mean,
- harmonic mean,
- contra-harmonic mean

FullText(HTML)

References(18)

References

[1]	YANG Z H, WU L M, CHU Y M. Optimal power mean bounds for Yang mean [J]. J Inequal Appl, 2014, 401: 1-10.
[2]	LI J F, YANG Z H, CHU Y M. Optimal power mean bounds for the second Yang mean [J]. J Inequal Appl, 2016, 31: 1-9.
[3]	QIAN W M, CHU Y M. Best possible bounds for Yang mean using generalized logarithmic mean [J]. Math Probl Eng, 2016, Article ID 8901258.
[4]	QIAN W M, CHU Y M, ZHANG X H. Sharp one-parameter mean bounds for Yang mean [J]. Mathematical Problems in Engineering, 2016, Article ID 1579468.
[5]	ZHOU S S, QIAN W M, CHU Y M, et al. Sharp power-type Heronian mean bounds for the Sándor and Yang means [J]. J Inequal Appl, 2015, 159: 1-10.
[6]	VUORINEN M. Hypergeometric Functions in Geometric Function Theory, Special Functions and Differential Equations [M]. New Delhi: Allied Publ, 1998.
[7]	裘松良, 沈洁敏. 关于平均值的两个问题 [J]. 杭州电子工业学院学报, 1997, 17(3): 1-7.
[8]	YANG Z H. Three families of two-parameter means constructed by trigonometric functions [J]. J Inequal Appl, 2013, 541: 1-27.
[9]	WANG J L, XU H Z, QIAN W M. Sharp bounds for Sándor-Yang means in terms of Lehmer means [J]. Adv Inequal Appl, 2018, 2: 1-8.
[10]	NEUMAN E. On a new family of bivariate means [J]. J Math Inequal, 2017, 11(3): 673-681.
[11]	YANG Z H, CHU Y M. Optimal evaluations for the Sándor-Yang mean by power mean [J]. Math Inequal Appl, 2016, 19(3): 1031-1038.
[12]	ZHAO T H, QIAN W M, SONG Y Q. Optimal bounds for two Sándor-type means in terms of power means [J]. J Inequal Appl, 2016, 64: 1-10.
[13]	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 (English version), 2016, 32(4): 352-358.
[14]	QIAN W M, XU H Z, CHU Y M. Improvements of bounds for the Sándor-Yang means [J]. J Inequal Appl, 2019, 73: 1-8.
[15]	XU H Z, CHU Y M, QIAN W M, Sharp bounds for the Sándor-Yang means in terms of arithmetic and contra-harmonic means [J]. J Inequal Appl, 2018, 127: 1-13.
[16]	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): 41-50. DOI: 10.3969/j.issn.1000-5641.2017.04.004.
[17]	XU H Z, QIAN W M. Sharp bounds for Sándor-Yang means in terms of quadratic mean [J]. J Math Inequal, 2018, 12(4): 1149-1158.
[18]	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.