Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan
In this paper, we show that the m-weighted arithmetic mean is greater than the product of the m-weighted geometric mean and Specht’s ratio. As a corollary, we also show that the m-weighted geometric mean is greater than the product of the m-weighted harmonic mean and Specht’s ratio.These results give the improvements for the classical Young inequalities, since Specht’s ratio is generally greater than 1. In addition, we give an operator inequality for positive operators, applying our refined Young inequality.
Furuich, S. (2012). Refined Young inequalities with Specht’s ratio. Journal of the Egyptian Mathematical Society, 20(1), 46-49. doi: 10.1016/j.joems.2011.12.010
MLA
Shigeru Furuich. "Refined Young inequalities with Specht’s ratio", Journal of the Egyptian Mathematical Society, 20, 1, 2012, 46-49. doi: 10.1016/j.joems.2011.12.010
HARVARD
Furuich, S. (2012). 'Refined Young inequalities with Specht’s ratio', Journal of the Egyptian Mathematical Society, 20(1), pp. 46-49. doi: 10.1016/j.joems.2011.12.010
VANCOUVER
Furuich, S. Refined Young inequalities with Specht’s ratio. Journal of the Egyptian Mathematical Society, 2012; 20(1): 46-49. doi: 10.1016/j.joems.2011.12.010
)
View on SCiNiTO