Open Access

On Shafer-Fink-Type Inequality

Journal of Inequalities and Applications20072007:067430

https://doi.org/10.1155/2007/67430

Received: 5 January 2007

Accepted: 14 April 2007

Published: 10 July 2007

Abstract

A new simple proof of Shafer-Fink-type inequality proposed by Malešević is given.

[12345678910]

Authors’ Affiliations

(1)
Department of Mathematics, Zhejiang Gongshang University

References

  1. Mitrinović DS: Analytic Inequalities, Die Grundlehren der Mathematischen Wisenschaften, Band 165. Springer, New York, NY, USA; 1970:xii+400.Google Scholar
  2. Fink AM: Two inequalities. Univerzitet u Beogradu. Publikacije Elektrotehničkog Fakulteta 1995, 6: 48–49.MathSciNetMATHGoogle Scholar
  3. Zhu L: On Shafer-Fink inequalities. Mathematical Inequalities & Applications 2005,8(4):571–574.MathSciNetView ArticleMATHGoogle Scholar
  4. Zhu L: A solution of a problem of Oppeheim. Mathematical Inequalities & Applications 2007,10(1):57–61.MathSciNetView ArticleMATHGoogle Scholar
  5. Malešević BJ: One method for proving inequalities by computer. Journal of Inequalities and Applications 2007, 2007: 8.Google Scholar
  6. Malešević BJ: An application of-method on inequalities of Shafer-Fink's type. to appear in Mathematical Inequalities & Applications to appear in Mathematical Inequalities & ApplicationsGoogle Scholar
  7. Malešević BJ: Some improvements of one method for proving inequalities by computer. preprint, 2007, http://arxiv.org/abs/math/0701020 preprint, 2007,
  8. Anderson GD, Vamanamurthy MK, Vuorinen MK: Conformal Invariants, Inequalities, and Quasiconformal Maps, Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons, New York, NY, USA; 1997:xxviii+505.Google Scholar
  9. 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
  10. Pinelis I: L'hospital type results for monotonicity, with applications. Journal of Inequalities in Pure and Applied Mathematics 2002,3(1, Article 5):5.MathSciNetGoogle Scholar

Copyright

© Ling 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.