Abstract and Applied Analysis

Refinements of Bounds for Neuman Means

Yu-Ming Chu and Wei-Mao Qian

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Abstract

We present the sharp bounds for the Neuman means S H A , S A H , S C A and S A C in terms of the arithmetic, harmonic, and contraharmonic means. Our results are the refinements or improvements of the results given by Neuman.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 354132, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273250

Digital Object Identifier
doi:10.1155/2014/354132

Mathematical Reviews number (MathSciNet)
MR3186960

Zentralblatt MATH identifier
07022209

Citation

Chu, Yu-Ming; Qian, Wei-Mao. Refinements of Bounds for Neuman Means. Abstr. Appl. Anal. 2014 (2014), Article ID 354132, 8 pages. doi:10.1155/2014/354132. https://projecteuclid.org/euclid.aaa/1412273250


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References

  • B. C. Carlson, “Algorithms involving arithmetic and geometric means,” The American Mathematical Monthly, vol. 78, pp. 496–505, 1971.
  • J. M. Borwein and P. B. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, John Wiley & Sons, New York, NY, USA, 1987.
  • E. Neuman and J. Sándor, “On the Schwab-Borchardt mean,” Mathematica Pannonica, vol. 14, no. 2, pp. 253–266, 2003.
  • E. Neuman and J. Sándor, “On the Schwab-Borchardt mean. II,” Mathematica Pannonica, vol. 17, no. 1, pp. 49–59, 2006.
  • E. Neuman, “A note on a certain bivariate mean,” Journal of Mathematical Inequalities, vol. 6, no. 4, pp. 637–643, 2012.
  • Y.-M. Chu and B.-Y. Long, “Bounds of the Neuman-Sándor mean using power and identric means,” Abstract and Applied Analysis, vol. 2013, Article ID 832591, 6 pages, 2013.
  • T.-H. Zhao, Y.-M. Chu, and B.-Y. Liu, “Optimal bounds for Neuman-Sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic means,” Abstract and Applied Analysis, vol. 2012, Article ID 302635, 9 pages, 2012.
  • E. Neuman, “On some means derived from the Schwab-Borchardt mean,” Journal of Mathematical Inequalities, Preprint, http://files.ele-math.com/preprints/jmi-1210-pre.pdf.
  • E. Neuman, “On some means derived from the Schwab-Borchardt mean II,” Journal of Mathematical Inequalities, Preprint, http://files.ele-math.com/preprints/jmi-1289-pre.pdf.
  • Z.-Y. He, Y.-M. Chu, and M.-K. Wang, “Optimal Bounds for Neuman Means in terms of harmonic and contraharmonic means,” Journal of Applied Mathematics, vol. 2013, Article ID 807623, 4 pages, 2013. \endinput