Open Access

Extension of Oppenheim's Problem to Bessel Functions

Journal of Inequalities and Applications20082007:082038

Received: 10 September 2007

Accepted: 22 October 2007

Published: 16 January 2008


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.


Authors’ Affiliations

Faculty of Economics, Babeş-Bolyai University
Department of Mathematics, Zhejiang Gongshang University


  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. 10.2307/2308467MathSciNetView ArticleGoogle 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. 10.2307/2310072MathSciNetView ArticleGoogle Scholar
  4. Zhu L: A solution of a problem of oppeheim. Mathematical Inequalities & Applications 2007,10(1):57–61.MathSciNetView ArticleGoogle 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 MathematicaeGoogle Scholar
  6. Baricz Á: Some inequalities involving generalized Bessel functions. Mathematical Inequalities & Applications 2007,10(4):827–842.MathSciNetView ArticleMATHGoogle 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.MathSciNetView ArticleMATHGoogle 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 MathematicsGoogle Scholar
  10. Zhu L: On shafer-fink inequalities. Mathematical Inequalities & Applications 2005,8(4):571–574.MathSciNetView ArticleMATHGoogle Scholar
  11. Zhu L: On Shafer-Fink-type inequality. Journal of Inequalities and Applications 2007, 2007: 4 pages.View ArticleMathSciNetMATHGoogle Scholar
  12. Malešević BJ: One method for proving inequalities by computer. Journal of Inequalities and Applications 2007, 2007: 8 pages.MathSciNetMATHGoogle Scholar
  13. Malešević BJ: An application of-method on inequalities of Shafer-Fink's type. Mathematical Inequalities & Applications 2007,10(3):529–534.MathSciNetMATHGoogle Scholar


© Á, Baricz and L. Zhu 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.