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Mat. Zametki, 2013, Volume 93, Issue 3, Pages 401–406 (Mi mz8905)  

This article is cited in 13 scientific papers (total in 13 papers)

A Refinement of the Becker–Stark Inequalities

Ling Zhu

Zhejiang Gongshang University

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.

DOI: https://doi.org/10.4213/mzm8905

Full text: PDF file (391 kB)
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English version:
Mathematical Notes, 2013, 93:3, 421–425

Bibliographic databases:

UDC: 517
Received: 20.05.2009
Revised: 03.05.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. Debnath, C. Mortici, L. Zhu, “Refinements of Jordan-Stečkin and Becker-Stark inequalities”, Results Math., 67:1-2 (2015), 207–215  crossref  mathscinet  zmath  isi
    2. Yu. Nishizawa, “Sharp Becker-Stark's type inequalities with power exponential functions”, J. Inequal. Appl., 2015, 402, 11 pp.  crossref  mathscinet  zmath  isi
    3. M. Mahmoud, “On a conjecture of double inequality for the tangent function”, Hacet. J. Math. Stat., 45:1 (2016), 43–48  crossref  mathscinet  zmath  isi  scopus
    4. Yu. Nishizawa, “Extended constant parts of Becker-Stark's and Shafer-Fink's inequalities”, Tamkang J. Math., 47:4 (2016), 385–391  crossref  mathscinet  zmath  isi
    5. Yu. Nishizawa, “Refined quadratic estimations of Shafer's inequality”, J. Inequal. Appl., 2017, 40, 11 pp.  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. Yu. Nishizawa, “Sharp exponential approximate inequalities for trigonometric functions”, Results Math., 71:3-4 (2017), 609–621  crossref  mathscinet  zmath  isi
    8. 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
    9. L. Zhu, “New bounds for the exponential function with cotangent”, J. Inequal. Appl., 2018, 106, 13 pp.  crossref  mathscinet  zmath  isi
    10. 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
    11. 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
    12. Chen X.-D., Ma J., Li Y., “Approximating Trigonometric Functions By Using Exponential Inequalities”, J. Inequal. Appl., 2019, 53  crossref  mathscinet  isi  scopus
    13. 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  isi
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