A Generalized Singular Value Inequality for Heinz Means

In this paper we will generalize a singular value inequality that was proved before. In particular we obtain an inequality for numerical radius as follows: \begin{equation*} 2 \sqrt{t (1-t)} \omega(t A^{\nu}B^{1-\nu}+(1-t)A^{1-\nu}B^{\nu}) \leq \omega(t A + (1- t) B), \end{equation*} where, $A$ and $B$ are positive semidefinite matrices, $ 0 \leq t \leq 1 $ and \\ $ 0 \leq \nu \leq \frac{3}{2}.$