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Matematicheskie Zametki, 2013, Volume 93, Issue 3, Pages 401–406
DOI: https://doi.org/10.4213/mzm8905
(Mi mzm8905)
 

This article is cited in 25 scientific papers (total in 25 papers)

A Refinement of the Becker–Stark Inequalities

Ling Zhu

Zhejiang Gongshang University
References:
Abstract: In this paper, a refinement of the Becker–Stark inequalities is established and a simple proof of this new inequality is given.
Keywords: Bernoulli numbers, Riemann's zeta function, power series expansion, upper and lower bounds, Becker–Stark inequalities.
Received: 20.05.2009
Revised: 03.05.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 3, Pages 421–425
DOI: https://doi.org/10.1134/S0001434613030085
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Ling Zhu, “A Refinement of the Becker–Stark Inequalities”, Mat. Zametki, 93:3 (2013), 401–406; Math. Notes, 93:3 (2013), 421–425
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm8905
  • https://doi.org/10.4213/mzm8905
  • https://www.mathnet.ru/eng/mzm/v93/i3/p401
  • This publication is cited in the following 25 articles:
    1. Suxia Wang, Tiehong Zhao, “New refinements of Becker-Stark inequality”, MATH, 9:7 (2024), 19677  crossref
    2. R. M. Dhaigude, Y. J. Bagul, “A note on the Becker-Stark type inequalities”, Probl. anal. Issues Anal., 11(29):1 (2022), 58–66  mathnet  crossref  mathscinet
    3. Zhu L., “New Sharp Double Inequality of Becker-Stark Type”, Mathematics, 10:4 (2022), 558  crossref  isi
    4. Chen X.-D., Wang H., Yang K., Xie J., “New Bounds of Wilker- and Huygens-Type Inequalities For Inverse Trigonometric Functions”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 115:1 (2021), 36  crossref  mathscinet  isi
    5. Chen X.-D., Yang K., Gong S., Zhu L., “A Family of Wilker'S Inequalities in Two Parameters and Its Applications”, J. Math. Inequal., 15:1 (2021), 421–441  crossref  mathscinet  isi  scopus
    6. Zhu L., “New Bounds For the Sine Function and Tangent Function”, Mathematics, 9:19 (2021), 2373  crossref  isi
    7. Wu Y., Bercu G., “New Refinements of Becker-Stark and Cusa-Huygens Inequalities Via Trigonometric Polynomials Method”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 115:2 (2021), 87  crossref  mathscinet  isi
    8. Zhu L., “Sharp Refined Quadratic Estimations of Shafer'S Inequalities”, AIMS Math., 6:5 (2021), 5020–5027  crossref  mathscinet  isi
    9. Zhu L., “New Bounds For the Ratio of Two Adjacent Even-Indexed Bernoulli Numbers”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 114:2 (2020), 83  crossref  mathscinet  isi
    10. Zhu L., “Monotonicities of Some Functions Involving Multiple Logarithm Function and Their Applications”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 114:3 (2020), 139  crossref  mathscinet  isi
    11. Chen X.-D., Ma J., Li Y., “Approximating Trigonometric Functions By Using Exponential Inequalities”, J. Inequal. Appl., 2019, 53  crossref  mathscinet  isi  scopus
    12. Chen Ch.-P., Elezovic N., “Generalizations and Refinements of Steckin-Type Inequality For Tangent and Secant Functions”, J. Math. Inequal., 13:2 (2019), 505–526  crossref  mathscinet  isi  scopus
    13. Zhang B., Chen Ch.-P., “Sharpness and Generalization of Jordan, Becker-Stark and Papenfuss Inequalities With An Application”, J. Math. Inequal., 13:4 (2019), 1209–1234  crossref  mathscinet  isi
    14. M. Nenezic, L. Zhu, “Some improvements of Jordan-Steckin and Becker-Stark inequalities”, Appl. Anal. Discret. Math., 12:1 (2018), 244–256  crossref  mathscinet  isi  scopus
    15. L. Zhu, “New bounds for the exponential function with cotangent”, J. Inequal. Appl., 2018, 106, 13 pp.  crossref  mathscinet  zmath  isi
    16. X.-D. Chen, J. Ma, J. Jin, Y. Wang, “A two-point-Padé-approximant-based method for bounding some trigonometric functions”, J. Inequal. Appl., 2018, 140, 15 pp.  crossref  mathscinet  isi  scopus
    17. Ch.-P. Chen, N. Elezovic, “Sharp Redheffer-type and Becker-Stark-type inequalities with an application”, Math. Inequal. Appl., 21:4 (2018), 1059–1078  crossref  mathscinet  zmath  isi  scopus
    18. Yu. Nishizawa, “Refined quadratic estimations of Shafer's inequality”, J. Inequal. Appl., 2017, 40, 11 pp.  crossref  mathscinet  zmath  isi  scopus
    19. Ch.-P. Chen, R. B. Paris, “Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities, I”, Math. Inequal. Appl., 20:4 (2017), 1003–1016  crossref  mathscinet  zmath  isi
    20. Yu. Nishizawa, “Sharp exponential approximate inequalities for trigonometric functions”, Results Math., 71:3-4 (2017), 609–621  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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