Skip to content

Advertisement

Journal of Inequalities and Applications
Journal of Inequalities and Applications Cover Image
  • Research Article
  • Open Access

On the Strengthened Jordan's Inequality

Journal of Inequalities and Applications20082007:074328

https://doi.org/10.1155/2007/74328

©  J.-L. Li and Y.-L. Li. 2007

  • Received: 21 July 2007
  • Accepted: 22 November 2007
  • Published:

Abstract

The main purpose of this paper is to present two methods of sharpening Jordan's inequality. The first method shows that one can obtain new strengthened Jordan's inequalities from old ones. The other method shows that one can sharpen Jordan's inequality by choosing proper functions in the monotone form of L'Hopital's rule. Finally, we improve a related inequality proposed early by Redheffer.

Keywords

  • Proper Function
  • Related Inequality
  • Monotone Form

[123456789101112131415]

Authors’ Affiliations

(1)
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China

References

  1. Mitrinović DS: Analytic Inequalities. Springer, New York, NY, USA; 1970:xii+400.View ArticleMATHGoogle Scholar
  2. Debnath L, Zhao C-J: New strengthened Jordan's inequality and its applications. Applied Mathematics Letters 2003,16(4):557–560. 10.1016/S0893-9659(03)00036-3MathSciNetView ArticleMATHGoogle Scholar
  3. Mercer AMcD, Abel U, Caccia D: Problems and solutions: solutions of elementary problems: E2952. The American Mathematical Monthly 1986,93(7):568–569. 10.2307/2323042MathSciNetView ArticleGoogle Scholar
  4. Özban AY: A new refined form of Jordan's inequality and its applications. Applied Mathematics Letters 2006,19(2):155–160. 10.1016/j.aml.2005.05.003MathSciNetView ArticleMATHGoogle Scholar
  5. Anderson GD, Qiu S-L, Vamanamurthy MK, Vuorinen M: Generalized elliptic integrals and modular equations. Pacific Journal of Mathematics 2000,192(1):1–37. 10.2140/pjm.2000.192.1MathSciNetView ArticleGoogle Scholar
  6. Zhu L: Sharpening Jordan's inequality and the Yang Le inequality. Applied Mathematics Letters 2006,19(3):240–243. 10.1016/j.aml.2005.06.004MathSciNetView ArticleMATHGoogle Scholar
  7. Zhu L: Sharpening Jordan's inequality and Yang Le inequality—II. Applied Mathematics Letters 2006,19(9):990–994. 10.1016/j.aml.2005.11.011MathSciNetView ArticleMATHGoogle Scholar
  8. Wu S, Debnath L: A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality. Applied Mathematics Letters 2006,19(12):1378–1384. 10.1016/j.aml.2006.02.005MathSciNetView ArticleMATHGoogle Scholar
  9. Wu S, Debnath L: A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality—II. Applied Mathematics Letters 2007,20(5):532–538. 10.1016/j.aml.2006.05.022MathSciNetView ArticleMATHGoogle Scholar
  10. Li J-L: An identity related to Jordan's inequality. International Journal of Mathematics and Mathematical Sciences 2006, 2006: 6 pages.Google Scholar
  11. Redheffer R, Ungar P, Lupas A, et al.: Problems and solutions: advanced problems: 5642,5665–5670. The American Mathematical Monthly 1969,76(4):422–423. 10.2307/2316453MathSciNetView ArticleGoogle Scholar
  12. Williams JP: Problems and solutions: solutions of advanced problems: 5642. The American Mathematical Monthly 1969,76(10):1153–1154.Google Scholar
  13. Li J-L: On a series of Erdős-Turán type. Analysis 1992,12(3–4):315–317.MathSciNetMATHGoogle Scholar
  14. Young RM: An Introduction to Nonharmonic Fourier Series, Pure and Applied Mathematics. Volume 93. Academic Press, New York, NY, USA; 1980:x+246.Google Scholar
  15. Li J-L: Spectral self-affine measures in . Proceedings of the Edinburgh Mathematical Society 2007,50(1):197–215. 10.1017/S0013091503000324MathSciNetView ArticleGoogle Scholar

Copyright

© J.-L. Li and Y.-L. Li. 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.

Advertisement