  In this paper, we study refinements of some inequalities related to Young
inequality for scalar and for operator. As our main results, we show refined
Young inequalities for two positive operators. This results refine the ordering
relations among the arithmetic mean, the geometric mean and the harmonic mean.
Finally, we give supplements for refined Young inequalities for two positive
real numbers. And then we also give operator inequalities based on the
supplemental inequalities.
