Geodesic
Refinements of bounds for Neuman means with applications
Yang, Yue-Ying1 ; Qian, Wei-Mao2 ; Chu, Yu-Ming3
1 School of Mechanical and Electrical Engineering, Huzhou Vocational & Technical College, Huzhou 313000, China
2 School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China
3 Department of Mathematics, Huzhou University, Huzhou 313000, China
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 4, p. 1529-1540.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.009.04.11
Classification : 26E60
Keywords: Neuman mean, Schwab-Borchardt mean, harmonic mean, geometric mean, quadratic mean, contra-harmonic mean, arithmetic mean.

Yang, Yue-Ying 1 ; Qian, Wei-Mao 2 ; Chu, Yu-Ming 3

1 School of Mechanical and Electrical Engineering, Huzhou Vocational & Technical College, Huzhou 313000, China
2 School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China
3 Department of Mathematics, Huzhou University, Huzhou 313000, China 
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Yang, Yue-Ying; Qian, Wei-Mao; Chu, Yu-Ming. Refinements of bounds for Neuman means with applications. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 4, p. 1529-1540. doi : 10.22436/jnsa.009.04.11. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.04.11/

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

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

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

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

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

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

[7] Zhang, Y.; Chu, Y. M.; Jiang, Y.-L. Sharp geometric mean bounds for Neuman means, Abstr. Appl. Anal., Volume 2014 (2014), pp. 1-6

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