$A \geq B \geq {0}$ iff $\left( {B^r A^p B^r} \right)^{1/q} \geq B^{\left( {p + 2r} \right)/q} $ for $r \geq {0},p \geq{0},q \geq 1$ with $\left( {1 + 2r} \right)q \geq p + 2r$ | Zendy

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

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