Refined Young inequalities with Specht's ratio

By Shigeru Furuichi. 2010

79 citations recorded by the source corpus.

In this paper, we show that the $\nu$-weighted arithmetic mean is greater than the product of the $\nu$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $\nu$-weighted geometric mean is greater than the product of the $\nu$-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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b2ee2f720548190b08342bec4636449322e1ea61

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In Applied Mathematics

1. Junliang Wu
2. Jianguo Zhao
3. Wenshi Liao
4. Nicucsor Minculete
5. Shigeru Furuichi

Citations in the corpus

• Alternative reverse inequalities for Young's inequality (2011, background): “See [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] for improvements of Young’s inequality and their recent advances.”
• NEW VERSIONS OF REVERSE YOUNG AND HEINZ MEAN INEQUALITIES WITH THE KANTOROVICH CONSTANT (2015, result): “For more results on the Young and Heinz mean inequalities, see[7], [11]and [12].”