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Journal of Applied Mathematics
Volume 2013, Article ID 582504, 7 pages
Research Article

Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means

1School of Architecture Engineering, Huzhou Vocational & Technical College, Huzhou 313000, China
2School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, China
3Department of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China

Received 10 October 2013; Revised 27 November 2013; Accepted 27 November 2013

Academic Editor: Juan Manuel Peña

Copyright © 2013 Fan Zhang 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.


We present the largest values , , and and the smallest values , , and such that the double inequalities , , and hold for all with , where , , , and denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of and , respectively.