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T Ando (1995)
Matrix Young inequalityOper. Theory Adv. Appl., 75
S. Furuichi, Minghua Lin (2010)
On refined Young inequalitiesarXiv: Functional Analysis
F. Kittaneh (1993)
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F. Kittaneh, Yousef Manasrah (2010)
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Hong-liang Zuo, Guanghua Shi, M. Fujii (2011)
REFINED YOUNG INEQUALITY WITH KANTOROVICH CONSTANTJournal of Mathematical Inequalities
RA Horn, CR Johnson (1985)
Matrix Analysis
We prove that if $$a,b>0$$ a , b > 0 and $$0\le \nu \le 1$$ 0 ≤ ν ≤ 1 , then for $$m=1,2,3,\ldots $$ m = 1 , 2 , 3 , … , we have $$\begin{aligned} \left( a^{\nu }b^{1-\nu }\right) ^{m}+r_{0}^{m}\left( a^{\frac{m}{2}}-b^{\frac{m}{2}}\right) ^{2}\le \Big ( \nu a+(1-\nu )b\Big ) ^{m}, \end{aligned}$$ a ν b 1 - ν m + r 0 m a m 2 - b m 2 2 ≤ ( ν a + ( 1 - ν ) b ) m , where $$r_{0}=\min \left\{ \nu ,1-\nu \right\} $$ r 0 = min ν , 1 - ν . This is a considerable generalization of two refinements of the classical Young inequality due to Kittaneh and Manasrah, and Hirzallah and Kittaneh, which correspond to the cases $$m=1$$ m = 1 and $$m=2$$ m = 2 , respectively. As applications of this inequality, we give refined Young-type inequalities for the traces, determinants, and norms of positive definite matrices.
Positivity – Springer Journals
Published: Feb 4, 2015
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