On refined Young inequalities

Abstract

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.

This paper has been withdrawn by the authors. The contents were unified in 1001.0535