JAMP  Vol.1 No.5 , November 2013
An Optimal Inequality for One-Parameter Mean
Abstract: In the present paper, we answer the question: for 0 < α < 1 fixed, what are the greatest value p(a) and the least value q(a) such that the inequality. For more information about abstract,please download the PDF file.
Cite this paper: Gao, H. , Zhang, Y. and Wang, T. (2013) An Optimal Inequality for One-Parameter Mean. Journal of Applied Mathematics and Physics, 1, 45-48. doi: 10.4236/jamp.2013.15006.

[1]   H. Y. Gao and W. J. Niu, “Sharp Inequalities Related to One-Parameter Mean and Gini Mean,” Journal of Mathematical Inequalities, Vol. 6, No. 4, 2012, pp. 545-555.

[2]   W. Cheung and F. Qi, “Logarithmic Convexity of the One-Parameter Mean Values,” Taiwanese Journal of Mathematics, Vol. 11, No. 1, 2007, pp. 231-237.

[3]   M. K. Wang, Y. F. Qiu and Y. M. Chu, “An Optimal Double Inequality among the One-Parameter, Arithmetic and Harmonic Means,” Revue d’Analyse Numerique et de Theorie de l’Approximation, Vol. 39, No. 2, 2012, pp. 169-175.

[4]   H. N. Hu, G. Y. Tu and Y. M. Chu, “Optimal Bouds for the Seiffert Mean in Terms of One-Parameter Means,” Journal of Applied Mathematics, 2012, Article ID: 917120.

[5]   B. Y. Long and Y. M. Chu, “Optimal Inequalities for Generalized Logarithmic, Arithmetic and Geometric Mean,” Journal of Inequalities and Applications, 2010, Article ID: 806825.

[6]   N. G. Zheng, Z. H. Zhang and X. M. Zhang, “Schur-Convexity of Two Types of One-Parameter Mean Values in Variables,” Journal of Inequalities and Applications, 2007, Article ID: 78175.