- Research Article
- Open Access
Extension of Oppenheim's Problem to Bessel Functions
Journal of Inequalities and Applications volume 2007, Article number: 082038 (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.
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
Mitrinović DS: Analytic inequalities, Die Grundlehren der Mathematischen Wisenschaften. Volume 1965. Springer, New York, NY, USA; 1970:xii+400.
Oppenheim A, Carver WB: Elementary problems and solutions: solutions: E1277. The American Mathematical Monthly 1958,65(3):206–209. 10.2307/2310072
Zhu L: A solution of a problem of oppeheim. Mathematical Inequalities & Applications 2007,10(1):57–61.
Baricz Á: Functional inequalities involving Bessel and modified Bessel functions of the first kind. to appear in Expositiones Mathematicae to appear in Expositiones Mathematicae
Baricz Á: Some inequalities involving generalized Bessel functions. Mathematical Inequalities & Applications 2007,10(4):827–842.
Watson GN: A treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge, UK; 1962.
Anderson GD, Vamanamurthy MK, Vuorinen M: Inequalities for quasiconformal mappings in space. Pacific Journal of Mathematics 1993,160(1):1–18.
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
Zhu L: On shafer-fink inequalities. Mathematical Inequalities & Applications 2005,8(4):571–574.
Zhu L: On Shafer-Fink-type inequality. Journal of Inequalities and Applications 2007, 2007: 4 pages.
Malešević BJ: One method for proving inequalities by computer. Journal of Inequalities and Applications 2007, 2007: 8 pages.
Malešević BJ: An application of-method on inequalities of Shafer-Fink's type. Mathematical Inequalities & Applications 2007,10(3):529–534.
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
- Bessel Function
- Modify Bessel Function
- Hyperbolic Analogue
- Trigonometric Inequality