Refined Young inequalities with Specht’s ratio
Furuich, S. (2012). Refined Young inequalities with Specht’s ratio. EKB Journal Management System, 20(1), 46-49. doi: 10.1016/j.joems.2011.12.010
Shigeru Furuich. "Refined Young inequalities with Specht’s ratio". EKB Journal Management System, 20, 1, 2012, 46-49. doi: 10.1016/j.joems.2011.12.010
Furuich, S. (2012). 'Refined Young inequalities with Specht’s ratio', EKB Journal Management System, 20(1), pp. 46-49. doi: 10.1016/j.joems.2011.12.010
Furuich, S. Refined Young inequalities with Specht’s ratio. EKB Journal Management System, 2012; 20(1): 46-49. doi: 10.1016/j.joems.2011.12.010

Refined Young inequalities with Specht’s ratio

Journal of the Egyptian Mathematical Society
Volume 20, Issue 1, 2012, Pages 46-49    PDF (343.42 K)
DOI: 10.1016/j.joems.2011.12.010
Author
Shigeru Furuich
Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan
Abstract
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.
Keywords
Specht’s ratio; Young inequality; Positive operator; Operator mean and operator inequality
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