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Mathematical Problems in Engineering
Volume 2016, Article ID 1579468, 5 pages
http://dx.doi.org/10.1155/2016/1579468
Research Article

Sharp One-Parameter Mean Bounds for Yang Mean

1School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China
2School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China

Received 19 July 2015; Accepted 9 February 2016

Academic Editor: Yann Favennec

Copyright © 2016 Wei-Mao Qian et al. 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. H. Alzer, Über eine Einparametrige Familie von Mittelwerten, Die Bayerische Akademie der Wissenschaften, 1988.
  2. W.-S. Cheung and F. Qi, “Logarithmic convexity of the one-parameter mean values,” Taiwanese Journal of Mathematics, vol. 11, no. 1, pp. 231–237, 2007. View at Google Scholar · View at MathSciNet · View at Scopus
  3. F. Qi, P. Cerone, S. S. Dragomir, and H. M. Srivastava, “Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 129–133, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. M.-K. Wang, Y.-F. Qiu, and Y.-M. Chu, “An optimal double inequality among the oneparameter, arithmetic and harmonic means,” Revue d'Analyse Numérique et de Théorie de l'Approximation, vol. 39, no. 2, pp. 169–175, 2010. View at Google Scholar
  5. Z.-Y. He, M.-K. Wang, and Y.-M. Chu, “Optimal one-parameter mean bounds for the convex combination of arithmetic and logarithmic means,” Journal of Mathematical Inequalities, vol. 9, no. 3, pp. 699–707, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  6. W.-F. Xia, S.-W. Hou, G.-D. Wang, and Y.-M. Chu, “Optimal one-parameter mean bounds for the convex combination of arithmetic and geometric means,” Journal of Applied Analysis, vol. 18, no. 2, pp. 197–207, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. H.-Y. Gao and W.-J. Niu, “Sharp inequalities related to one-parameter mean and Gini mean,” Journal of Mathematical Inequalities, vol. 6, no. 4, pp. 545–555, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H.-N. Hu, G.-Y. Tu, and Y.-M. Chu, “Optimal bounds for Seiffert mean in terms of one-parameter means,” Journal of Applied Mathematics, vol. 2012, Article ID 917120, 7 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. Y.-Q. Song, W.-F. Xia, X.-H. Shen, and Y.-M. Chu, “Bounds for the identric mean in terms of one-parameter mean,” Applied Mathematical Sciences, vol. 7, no. 88, pp. 4375–4386, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. W.-F. Xia, G.-D. Wang, Y.-M. Chu, and S.-W. Hou, “Sharp inequalities between one-parameter and power means,” Advances in Mathematics, vol. 42, no. 5, pp. 713–722, 2013. View at Google Scholar · View at MathSciNet
  11. Z.-H. Yang, “Three families of two-parameter means constructed by trigonometric functions,” Journal of Inequalities and Applications, vol. 2013, article 541, 27 pages, 2013. View at Google Scholar · View at MathSciNet
  12. Z.-H. Yang, Y.-M. Chu, Y.-Q. Song, and Y.-M. Li, “A sharp double inequality for trigonometric functions and its applications,” Abstract and Applied Analysis, vol. 2014, Article ID 592085, 9 pages, 2014. View at Publisher · View at Google Scholar
  13. Z.-H. Yang, L.-M. Wu, and Y.-M. Chu, “Optimal power mean bounds for Yang mean,” Journal of Inequalities and Applications, vol. 2014, article 401, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S.-S. Zhou, W.-M. Qian, Y.-M. Chu, and X.-H. Zhang, “Sharp power-type Heronian mean bounds for the Sándor and Yang means,” Journal of Inequalities and Applications, vol. 2015, article 159, 10 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet