Complementary inequalities to improved AM-GM inequality
Complementary inequalities to improved AM-GM inequality
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DOI：
10.1007/s10114-017-7118-y
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发表时间：
2017-06
期刊：
影响因子：
--
通讯作者：
H. Moradi;M. Omidvar
中科院分区：
文献类型：
--
作者：
H. Moradi;M. Omidvar
Following an idea of Lin, we prove that ifandbe two positive operators such that, then \begin{equation*} {{\Phi }^{2}}\left( \frac{A+B}{2} \right)\le \frac{{{K}^{2}}\left( h \right)}{{{\left( 1+\frac{{{\left( \log \frac{M'}{m'} \right)}^{2}}}{8} \right)}^{2}}}{{\Phi }^{2}}\left( A\#B \right), \end{equation*} and \begin{equation*} {{\Phi }^{2}}\left( \frac{A+B}{2} \right)\le \frac{{{K}^{2}}\left( h \right)}{{{\left( 1+\frac{{{\left( \log \frac{M'}{m'} \right)}^{2}}}{8} \right)}^{2}}}{{\left( \Phi \left( A \right)\#\Phi \left( B \right) \right)}^{2}}, \end{equation*} whereandandis a positive unital linear map.
