About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 302635, 9 pages
http://dx.doi.org/10.1155/2012/302635
Research Article

Optimal Bounds for Neuman-Sándor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means

1Department of Mathematics, Hangzhou Normal University, Hangzhou 313036, China
2School of Mathematics and Computation Sciences, Hunan City University, Yiyang 413000, China
3School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

Received 15 October 2012; Accepted 5 December 2012

Academic Editor: Julian López-Gómez

Copyright © 2012 Tie-Hong Zhao 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.

Citations to this Article [16 citations]

The following is the list of published articles that have cited the current article.

  • Edward Neuman, “Sharp Inequalities Involving Neuman-Sandor And Logarithmic Means,” Journal of Mathematical Inequalities, vol. 7, no. 3, pp. 413–419, 2013. View at Publisher · View at Google Scholar
  • Yuming Chu, “Optimal Inequalities Between Neuman-Sandor, Centroidal And Harmonic Means,” Journal of Mathematical Inequalities, vol. 7, no. 4, pp. 593–600, 2013. View at Publisher · View at Google Scholar
  • Zhen-Hang Yang, “Estimates For Neuman-Sandor Mean By Power Means And Their Relative Errors,” Journal of Mathematical Inequalities, vol. 7, no. 4, pp. 711–726, 2013. View at Publisher · View at Google Scholar
  • Mustapha Raissouli, “Positive answer for a conjecture about stabilizable means,” Journal of Inequalities and Applications, 2013. View at Publisher · View at Google Scholar
  • Hui Sun, Xu-Hui Shen, Tie-Hong Zhao, and Yu-Ming Chu, “Optimal bounds for the neuman-sándor means in terms of geometric and contraharmonic means,” Applied Mathematical Sciences, vol. 7, no. 85-88, pp. 4363–4373, 2013. View at Publisher · View at Google Scholar
  • Tie-Hong Zhao, Yu-Ming Chu, Yun-Liang Jiang, and Yong-Min Li, “Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means,” Abstract and Applied Analysis, vol. 2013, pp. 1–12, 2013. View at Publisher · View at Google Scholar
  • Fan Zhang, Yu-Ming Chu, and Wei-Mao Qian, “Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means,” Journal of Applied Mathematics, vol. 2013, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Wei-Mao Qian, and Yu-Ming Chu, “On Certain Inequalities for Neuman-Sándor Mean,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Zai-Yin He, Yu-Ming Chu, and Miao-Kun Wang, “Optimal Bounds for Neuman Means in Terms of Harmonic and Contraharmonic Means,” Journal of Applied Mathematics, 2013. View at Publisher · View at Google Scholar
  • Yu-Ming Chu, and Bo-Yong Long, “Bounds of the Neuman-Sándor Mean Using Power and Identric Means,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Zai-Yin He, Wei-Mao Qian, Yun-Liang Jiang, Ying-Qing Song, and Yu-Ming Chu, “Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean,” Abstract and Applied Analysis, vol. 2013, pp. 1–5, 2013. View at Publisher · View at Google Scholar
  • Hui Sun, Tiehong Zhao, Yuming Chu, and Baoyu Liu, “A Note On The Neuman-Sandor Mean,” Journal of Mathematical Inequalities, vol. 8, no. 2, pp. 287–297, 2014. View at Publisher · View at Google Scholar
  • Edward Neuman, “On Some Means Derived From The Schwab-Borchardt Mean Ii,” Journal of Mathematical Inequalities, vol. 8, no. 2, pp. 359–368, 2014. View at Publisher · View at Google Scholar
  • Yuming Chu, Tiehong Zhao, and Yingqing Song, “Sharp bounds for neuman-sándor mean in terms of the convex combination of quadratic and first Seiffert means,” Acta Mathematica Scientia, vol. 34, no. 3, pp. 797–806, 2014. View at Publisher · View at Google Scholar
  • Edward Neuman, “On Some Means Derived From The Schwab-Borchardt Mean,” Journal of Mathematical Inequalities, vol. 8, no. 1, pp. 171–183, 2014. View at Publisher · View at Google Scholar
  • Yu-Ming Chu, and Wei-Mao Qian, “Refinements of Bounds for Neuman Means,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar