About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 425175, 6 pages
http://dx.doi.org/10.1155/2012/425175
Research Article

Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

1Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou 310012, China

Received 17 September 2011; Accepted 5 November 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Yu-Ming Chu and Shou-Wei Hou. 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.

Linked References

  1. Y.-M. Chu, M.-K. Wang, S.-L. Qiu, and Y.-F. Qiu, “Sharp generalized Seiffert mean bounds for Toader mean,” Abstract and Applied Analysis, vol. 2011, Article ID 605259, 8 pages, 2011. View at Publisher · View at Google Scholar
  2. S.-W. Hou and Y.-M. Chu, “Optimal convex combination bounds of root-square and harmonic root-square means for Seiffert mean,” International Journal of Mathematical Analysis, vol. 5, no. 39, pp. 1897–1904, 2011.
  3. H. Liu and X.-J. Meng, “The optimal convex combination bounds for Seiffert's mean,” Journal of Inequalities and Applications, vol. 2011, Article ID 686834, 9 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. J. Pahikkala, “On contraharmonic mean and Phythagorean triples,” Elementary Math, vol. 65, no. 2, pp. 62–67, 2010.
  5. S. Toader and Gh. Toader, “Complementaries of Greek means with respect to Gini means,” International Journal of Applied Mathematics & Statistics, vol. 11, no. N07, pp. 187–192, 2007. View at Zentralblatt MATH
  6. E. Neuman and J. Sáandor, “On the Schwab-Borchardt mean II,” Mathematica Pannonica, vol. 17, no. 1, pp. 49–59, 2006.
  7. Y. Lim, “The inverse mean problem of geometric mean and contraharmonic means,” Linear Algebra and its Applications, vol. 408, no. 1–3, pp. 221–229, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. S. Toader and Gh. Toader, “Generalized complementaries of Greek means,” Pure Mathematics and Applications, vol. 15, no. 2-3, pp. 335–342, 2004.
  9. E. Neuman and J. Sándor, “On the Schwab-Borchardt mean,” Mathematica Pannonica, vol. 14, no. 2, pp. 253–266, 2003. View at Zentralblatt MATH
  10. J. R. Siler, “Mean crowds and Pythagorean triples,” Fibonacci Quarterly, vol. 36, no. 4, pp. 323–326, 1998. View at Zentralblatt MATH · View at Scopus
  11. W. N. Anderson Jr., M. E. Mays, T. D. Morley, and G. E. Trapp, “The contraharmonic mean of HSD matrices,” SIAM Journal on Algebraic and Discrete Methods, vol. 8, no. 4, pp. 674–682, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. J. Seiffert, “Aufgabe β 16,” Die Wurzel, vol. 29, pp. 221–222, 1995.
  13. P. A. Hästö, “A monotonicity property of ratios of symmetric homogeneous means,” Journal of Inequalities in Pure and Applied Mathematics, vol. 3, no. 5, article 71, 23 pages, 2002.
  14. Y.-M. Chu, M.-K. Wang, and Y.-F. Qiu, “An optimal double inequality between power-type Heron and Seiffert means,” Journal of Inequalities and Applications, vol. 2010, Article ID 146945, 11 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. M.-K. Wang, Y.-F. Qiu, and Y.-M. Chu, “Sharp bounds for Seiffert means in terms of Lehmer means,” Journal of Mathematical Inequalities, vol. 4, no. 4, pp. 581–586, 2010. View at Zentralblatt MATH
  16. Y.-M. Chu, C. Zong, and G.-D. Wang, “Optimal convex combination bounds of Seiffert and geometric means for the arithmetic mean,” Journal of Mathematical Inequalities, vol. 5, no. 3, pp. 429–434, 2011.
  17. Y.-M. Chu, M.-K. Wang, and W.-M. Gong, “Two sharp double inequalities for Seiffert mean,” Journal of Inequalities and Applications, vol. 2011, article 44, 2011.