Abstract
Let $A , B$ be positive operators on a Hilbert space with $0 < m \le A, B \le M$. Then for every unital positive linear map $\varPhi $, $$ \varPhi ^2((A+B)/2)\le K^2(h)\varPhi ^{2}(A\mathbin {\sharp } B), $$ and $$ \varPhi ^2((A+B)/2)\le K^2(h)(\v
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