  In this paper, we show that the $\nu$-weighted arithmetic mean is greater
than the product of the $\nu$-weighted geometric mean and Specht's ratio. As a
corollary, we also show that the $\nu$-weighted geometric mean is greater than
the product of the $\nu$-weighted harmonic mean and Specht's ratio. These
results give the improvements for the classical Young inequalities, since
Specht's ratio is generally greater than 1. In addition, we give an operator
inequality for positive operators, applying our refined Young inequality.
