Skip to main content
  • Research Article
  • Open access
  • Published:

Extension of Oppenheim's Problem to Bessel Functions

Abstract

Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.

[12345678910111213]

References

  1. Ogilvy CS, Oppenheim A, Ivanoff VF, Ford LF Jr., Fulkerson DR, Narayanan VK Jr.: Elementary problems and solutions: problems for solution: E1275-E1280. The American Mathematical Monthly 1957,64(7):504–505. 10.2307/2308467

    Article  MathSciNet  Google Scholar 

  2. Mitrinović DS: Analytic inequalities, Die Grundlehren der Mathematischen Wisenschaften. Volume 1965. Springer, New York, NY, USA; 1970:xii+400.

    Google Scholar 

  3. Oppenheim A, Carver WB: Elementary problems and solutions: solutions: E1277. The American Mathematical Monthly 1958,65(3):206–209. 10.2307/2310072

    Article  MathSciNet  Google Scholar 

  4. Zhu L: A solution of a problem of oppeheim. Mathematical Inequalities & Applications 2007,10(1):57–61.

    Article  MathSciNet  Google Scholar 

  5. Baricz Á: Functional inequalities involving Bessel and modified Bessel functions of the first kind. to appear in Expositiones Mathematicae to appear in Expositiones Mathematicae

  6. Baricz Á: Some inequalities involving generalized Bessel functions. Mathematical Inequalities & Applications 2007,10(4):827–842.

    Article  MathSciNet  MATH  Google Scholar 

  7. Watson GN: A treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge, UK; 1962.

    Google Scholar 

  8. Anderson GD, Vamanamurthy MK, Vuorinen M: Inequalities for quasiconformal mappings in space. Pacific Journal of Mathematics 1993,160(1):1–18.

    Article  MathSciNet  MATH  Google Scholar 

  9. András Sz, Baricz Á: Monotonicity property of generalized and normalized Bessel functions of complex order. submitted to Journal of Inequalities in Pure and Applied Mathematics submitted to Journal of Inequalities in Pure and Applied Mathematics

  10. Zhu L: On shafer-fink inequalities. Mathematical Inequalities & Applications 2005,8(4):571–574.

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhu L: On Shafer-Fink-type inequality. Journal of Inequalities and Applications 2007, 2007: 4 pages.

    Article  MathSciNet  MATH  Google Scholar 

  12. Malešević BJ: One method for proving inequalities by computer. Journal of Inequalities and Applications 2007, 2007: 8 pages.

    MathSciNet  MATH  Google Scholar 

  13. Malešević BJ: An application of-method on inequalities of Shafer-Fink's type. Mathematical Inequalities & Applications 2007,10(3):529–534.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Árpád Baricz.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Baricz, Á., Zhu, L. Extension of Oppenheim's Problem to Bessel Functions. J Inequal Appl 2007, 082038 (2008). https://doi.org/10.1155/2007/82038

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/82038

Keywords