Research article

Refinements of Huygens- and Wilker- type inequalities

  • Received: 22 November 2019 Accepted: 11 March 2020 Published: 19 March 2020
  • MSC : Primary 26D15; Secondary 42A10

  • In this paper we give some refinements and sharpness of the Huygens- and Wilker- type inequalities, and show a proof of the second conjecture by Chen and Chueng in [10].

    Citation: Ling Zhu, Zhengjie Sun. Refinements of Huygens- and Wilker- type inequalities[J]. AIMS Mathematics, 2020, 5(4): 2967-2978. doi: 10.3934/math.2020191

    Related Papers:

  • In this paper we give some refinements and sharpness of the Huygens- and Wilker- type inequalities, and show a proof of the second conjecture by Chen and Chueng in [10].


    加载中


    [1] F. T. Campan, The Story of Number, Romania, 1977.
    [2] C. Mortici, The natural approach of Wilker-Cusa-Huygens inequalities, Math. Inequal. Appl., 14 (2011), 535-541.
    [3] J. B. Wilker, Problem E 3306, Amer. Math. Monthly, 96 (1989), 55.
    [4] Z.-H. Yang and Y.-M. Chu, Sharp Wilker-type inequalities with applications, J. Inequal. Appl., 2014 (2014), 166.
    [5] H.-H. Chu, Z.-H. Yang, Y.-M. Chu, et al. Generalized Wilker-type inequalities with two parameters, J. Inequal. Appl., 2016 (2016), 187.
    [6] H. Sun, Z.-H. Yang and Y.-M. Chu, Necessary and sufficient conditions for the two parameter generalized Wilker-type inequalities, J. Inequal. Appl., 2016 (2016), 322.
    [7] E. Neuman, On Wilker and Huygens type inequalities, Math. Inequal. Appl., 15 (2012), 271-279.
    [8] J. S. Sumner, A. A. Jagers, M. Vowe, et al. Inequalities involving trigonometric functions, Amer. Math. Monthly, 98 (1991), 264-267. doi: 10.2307/2325035
    [9] W.-D. Jiang, Q.-M. Luo, F. Qi, Refinements and sharpening of some Huygens and Wilker type inequalities, Turkish J. Anal. Number Theory, 2 (2014), 134-139. doi: 10.12691/tjant-2-4-6
    [10] Ch.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens Type Inequalities, J. Inequal. Appl., 2012 (2012), 72.
    [11] J.-L. Li, An identity related to Jordan's inequality, Int. J. Math. Math. Sci., 2006.
    [12] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, U. S. National Bureau of Standards, Washington, DC, USA, 1964.
    [13] A. Jeffrey, Handbook of Mathematical Formulas and Integrals, Elsevier Academic Press, San Diego, Calif, USA, 3rd edition, 2004.
    [14] C. D'Aniello, On some inequalities for the Bernoulli numbers, Rendiconti del Circolo Matematico di Palermo. Serie II, 43 (1994), 329-332. doi: 10.1007/BF02844246
    [15] H. Alzer, Sharp bounds for the Bernoulli numbers, Archiv der Mathematik, 74 (2000), 207-211. doi: 10.1007/s000130050432
    [16] Z.-H. Yang and J.-F. Tian, Sharp bounds for the ratio of two zeta functions, J. Comput. Appl. Math., 364 (2020), 112359.
    [17] F. Qi, A double inequality for the ratio of two non-zero neighbouring Bernoulli numbers, J. Comput. Appl. Math., 351 (2019), 1-5. doi: 10.1016/j.cam.2018.10.049
    [18] L. Zhu, New bounds for the ratio of two adjacent even-indexed Bernoulli numbers, RACSAM, 114 (2020), 83.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3595) PDF downloads(322) Cited by(8)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog