  In this article, we prove several multi-term refinements of Young type
inequalities for both real numbers and operators improving several known
results. Among other results, we prove \begin{eqnarray*}
A\#_{\nu}B&+&\sum_{j=1}^{N}s_{j}(\nu)\left(A\#_{\alpha_j(\nu)}B+A\#_{2^{1-j}+\alpha_j(\nu)}B-2A\#_{2^{-j}+\alpha_j(\nu)}B\right)\leq
A\nabla_{\nu}B, \end{eqnarray*} for the positive operators $A$ and $B$, where
$0\leq \nu\leq 1, N\in\mathbb{N}$ and $\alpha_j(\nu)$ is a certain function.
Moreover, some new Heinz type inequalities involving the Hilbert-Schmidt norm
are established.
