Refinements of bounds for Neuman means with applications

Volume 9, Issue 4, pp 1529--1540 http://dx.doi.org/10.22436/jnsa.009.04.11

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Authors

Yue-Ying Yang - School of Mechanical and Electrical Engineering, Huzhou Vocational & Technical College, Huzhou 313000, China. Wei-Mao Qian - School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China. Yu-Ming Chu - Department of Mathematics, Huzhou University, Huzhou 313000, China.

Abstract

In this article, we present the sharp bounds for the Neuman means derived from the Schwab-Borchardt, geometric, arithmetic and quadratic means in terms of the arithmetic and geometric combinations of harmonic, arithmetic and contra-harmonic means.

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Keywords

• Neuman mean
• Schwab-Borchardt mean
• harmonic mean
• geometric mean
• quadratic mean
• contra-harmonic mean
• arithmetic mean.

MSC

•  26E60

References

• [1] E. Neuman , On a new bivariate mean, Aequationes Math., 88 (2014), 277-289.


• [2] E. Neuman, J. Sándor, On the Schwab-Borchardt mean, Math. Pannon., 14 (2003), 253-266.


• [3] E. Neuman, J. Sándor , On the Schwab-Borchardt mean II, Math. Pannon., 17 (2006), 49-59.


• [4] W. M. Qian, Z. H. Shao, Y. M. Chu, Sharp inequalities involving Neuman means of the second kind, J. Math. Inequal., 9 (2015), 531-540.


• [5] Y. Y. Yang, W. M. Qian, The optimal convex combination bounds of harmonic, arithmetic and contraharmonic means for the Neuman means, Int. Math. Fourm, 9 (2014), 1295-1307.


• [6] L. Yang, Y. Y. Yang, Q. Wang, W.-M. Qian, The optimal geometric combination bounds for Neuman means of harmonic, arithmetic and contra-harmonic means, Pac. J. Appl. Math., 6 (2014), 283-292.


• [7] Y. Zhang, Y. M. Chu, Y.-L. Jiang, Sharp geometric mean bounds for Neuman means, Abstr. Appl. Anal., 2014 (2014), 6 pages.