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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 302635, 9 pages
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 [19 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.
- Yuming Chu, “Optimal Inequalities Between Neuman-Sandor, Centroidal And Harmonic Means,” Journal of Mathematical Inequalities, vol. 7, no. 4, pp. 593–600, 2013.
- 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.
- Mustapha Raissouli, “Positive answer for a conjecture about stabilizable means,” Journal of Inequalities and Applications, 2013.
- 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.
- 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.
- Wei-Mao Qian, and Yu-Ming Chu, “On Certain Inequalities for Neuman-Sándor Mean,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013.
- 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.
- 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.
- 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.
- 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.
- Yu-Ming Chu, Hua Wang, and Tie-Hong Zhao, “Sharp bounds for the Neuman mean in terms of the quadratic and second Seiffert means,” Journal Of Inequalities And Applications, 2014.
- 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.
- Edward Neuman, “On Some Means Derived From The Schwab-Borchardt Mean Ii,” Journal of Mathematical Inequalities, vol. 8, no. 2, pp. 359–368, 2014.
- 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.
- Edward Neuman, “On Some Means Derived From The Schwab-Borchardt Mean,” Journal of Mathematical Inequalities, vol. 8, no. 1, pp. 171–183, 2014.
- Yu-Ming Chu, and Wei-Mao Qian, “Refinements of Bounds for Neuman Means,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014.
- Zhen-Hang Yang, Yu-Ming Chu, and Miao-Kun Wang, “Monotonicity criterion for the quotient of power series with applications,” Journal of Mathematical Analysis and Applications, vol. 428, no. 1, pp. 587–604, 2015.
- Hao-Chuan Cui, Nan Wang, and Bo-Yong Long, “Optimal Bounds for the Neuman-Sándor Mean in terms of the Convex Combination of the First and Second Seiffert Means,” Mathematical Problems in Engineering, vol. 2015, pp. 1–6, 2015.