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Q4669828 - MaRDI portal

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Please use this page instead for the normal view: scientific article; zbMATH DE number 2157249

scientific article; zbMATH DE number 2157249

Language	Label	Description	Also known as
English	No label defined	scientific article; zbMATH DE number 2157249

Statements

scholarly article

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Takayuki Furuta

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publication date

15 April 2005

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zbMATH Keywords

Löwner-Heinz inequality

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Furuta inequality

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MaRDI profile type

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\(A\geqq B\geqq 0\) ensures \((A^{\frac{r}{2}}A^pA^{\frac{r}{2}})^{\frac{1}{q}}\geqq (A^{\frac{r}{2}}B^pA^{\frac{r}{2}})^{\frac{1}{q}}\) for \(p\geqq 0\), \(q\geqq 1\), \(r\geqq 0\) with \((1+r)q\geqq p+r\) and its applications

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\(A\geq B\geq 0\) ensures \((B^{\frac r2}A^pB^{\frac r2})^{\frac 1q}\geq(B^{\frac r2}B^pB^{\frac r2})^{\frac 1q}\) for \(r\geq 0\), \(p\geq 0\), \(q\geq 1\) with \((1+r)q\geq p+r\) and its recent applications

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$A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$

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A\(\geq B\geq 0\) iff \((B^ rA^ pB^ r)^{1/q}\geq B^{(p+2r)/q}\) for r\(\geq 0\), p\(\geq 0\), q\(\geq 1\) with \((1+2r)q\geq p+2r\)

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Relations between two inequalities \((B^{\frac r2} A^p B^{\frac r2})^{\frac r{p+r}}\geq B^r\) and \(A^p\geq(A^{\frac p2} B^r A^{\frac p2})^{\frac p{p+r}}\) and their applications

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Some inequalities for (a + b)<sup>p</sup> and (a + b)<sup>p</sup> + (a − b)<sup>p</sup>

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Identifiers

zbMATH Open document ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:4669828

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