Skip to main content
SpringerLink
Log in

Sharp Exponential Approximate Inequalities for Trigonometric Functions

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we give some exponential inequalities derived from the inequalities containing trigonometric functions presented by Cusa, Huygens, Chen and Sándor.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, C.-P., Cheung, W.-S.: Sharpness of Wilker and Huygens type inequalities. J. Inequal. Appl. (2012)

  2. Chen C.-P., Cheung W.-S.: Sharp Cusa and Becker–Stark inequalities. J. Inequal. Appl. 136, 6 (2011)

    MATH  Google Scholar 

  3. Chen C.-P., Sándor J.: Sharp inequalities for trigonometric and hyperbolic functions. J. Math. Inequal. 9(1), 203–217 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Debnath L., Mortici C., Zhu L.: Refinements of Jordan-Steckin and Becker–Stark inequalities. Results Math. 67(1–2), 207–215 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Mitrinović D.S.: Analytic Inequalities. Springer, Berlin (1970)

    Book  MATH  Google Scholar 

  6. Mortici C.: The natural approach of Wilker–Cusa–Huygens inequalities. Math. Inequal. Appl. 14, 535–541 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Neuman E.: On Wilker and Huygens type inequalities. Math. Inequal. Appl. 15(2), 271–279 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Neuman E., Sandor J.: On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa–Huygens, Wilker and Huygens inequalities. Math. Inequal. Appl. 13(4), 715–723 (2010)

    MathSciNet  MATH  Google Scholar 

  9. Nishizawa, Y.: Extended constant parts of Wilker types and Cusa–Huygens types inequalities, Far East J. Math. Sci. (2016, to appear)

  10. Sun Z.-J., Zhu L.: Simple proofs of the Cusa–Huygens-type and Becker–Stark-type inequalities. J. Math. Inequal. 7(4), 563–567 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhu L.: A refinement of the Becker–Stark inequalities. Math. Notes 93(3–4), 421–425 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhu, L.: Sharp Becker–Stark-type inequalities for Bessel functions. J. Inequal. Appl., Art. ID 838740 (2010)

  13. Zhu, L., Hua, J.: Sharpening the Becker–Stark inequalities. J. Inequal. Appl., Art. ID 931275 (2010)

Download references

Author information

Authors and Affiliations

  1. General Education, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi, 755-8555, Japan

    Yusuke Nishizawa

Authors
  1. Yusuke Nishizawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yusuke Nishizawa.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nishizawa, Y. Sharp Exponential Approximate Inequalities for Trigonometric Functions. Results Math 71, 609–621 (2017). https://doi.org/10.1007/s00025-016-0566-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-016-0566-3

Mathematics Subject Classification

Keywords

Search

Navigation