On certain inequalities for Neuman-Sándor mean. (English) Zbl 1276.26060

Qian, Wei-Mao; Chu, Yu-Ming

Abstr. Appl. Anal. 2013, Article ID 790783, 6 p. (2013).

Summary: We present several new sharp bounds for Neuman-Sándor mean in terms of arithmetic, centroidal, quadratic, harmonic root square, and contraharmonic means.

MSC:

26E60

Means

Keywords:

arithmetic, centroidal, quadratic, harmonic root square; contraharmonic means

References:

[1]	Neuman, E.; Sándor, J., On the Schwab-Borchardt mean, Mathematica Pannonica, 14, 2, 253-266 (2003) · Zbl 1053.26015
[2]	Neuman, E.; Sándor, J., On the Schwab-Borchardt mean. II, Mathematica Pannonica, 17, 1, 49-59 (2006) · Zbl 1100.26011
[3]	Li, Y.-M.; Long, B.-Y.; Chu, Y.-M., Sharp bounds for the Neuman-Sádor mean in terms of generalized logarithmic mean, Journal of Mathematical Inequalities, 6, 4, 567-577 (2012) · Zbl 1257.26031
[4]	Neuman, E., A note on a certain bivariate mean, Journal of Mathematical Inequalities, 6, 4, 637-643 (2012) · Zbl 1257.26013
[5]	Chu, Y.-M.; Long, B.-Y.; Gong, W.-M.; Song, Y.-Q., Sharp bounds for Seiffert and Neuman-Sándor means in terms of generalized logarithmic means, Journal of Inequalities and Applications, 2013 (2013) · Zbl 1282.26046 · doi:10.1186/1029-242X-2013-10
[6]	Chu, Y.-M.; Long, B.-Y., Bounds of the Neuman-Sándor mean using power and identric means, Abstract and Applied Analysis, 2013 (2013) · Zbl 1264.26038 · doi:10.1155/2013/832591
[7]	Zhao, T.-H.; Chu, Y.-M.; Liu, B.-Y., Optimal bounds for Neuman-Sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic means, Abstract and Applied Analysis (2012) · Zbl 1256.26018 · doi:10.1155/2012/302635
[8]	Zhao, T.-H.; Chu, Y.-M.; Jiang, Y.-L.; Li, Y.-M., Best possible bounds for Neuman-Sándor mean by the identric, quadratic and contraharmonic means, Abstract and Applied Analysis, 2013 (2013) · Zbl 1276.26065 · doi:10.1155/2013/348326
[9]	He, Z.-Y.; Qian, W.-M.; Jiang, Y.-L.; Song, Y.-Q.; Chu, Y.-M., Bounds for the combinations of Neuman-Sándor, arithmetic and second Seiffer means in terms of contraharmonic mean, Abstract and Applied Analysis, 2013 (2013) · Zbl 1272.26030 · doi:10.1155/2013/903982
[10]	Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M. K., Conformal Invariants, Inequalities, and Quasiconformal Maps. Conformal Invariants, Inequalities, and Quasiconformal Maps, Canadian Mathematical Society Series of Monographs and Advanced Texts, xxviii+505 (1997), New York, NY, USA: John Wiley & Sons, New York, NY, USA · Zbl 0885.30012
[11]	Simić, S.; Vuorinen, M., Landen inequalities for zero-balanced hypergeometric functions, Abstract and Applied Analysis, 2012 (2012) · Zbl 1241.26021 · doi:10.1155/2012/932061