Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate MeansReport as inadecuate




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Journal of Applied MathematicsVolume 2013 2013, Article ID 582504, 7 pages

Research Article

School of Architecture Engineering, Huzhou Vocational and Technical College, Huzhou 313000, China

School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, China

Department 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.

Abstract

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.





Author: Fan Zhang, Yu-Ming Chu, and Wei-Mao Qian

Source: https://www.hindawi.com/



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