SOME REFINEMENTS OF YOUNG TYPE INEQUALITIES.

In this paper, we study some improvements of Young type inequalities. We obtain some reverse improvements of Young inequality. Among other results, we show a refined Young inequality. For v ∈ [0, 1] and a, b > 0, then a∇_vb ≤ M_v^R (h)a♯_vb, where M_v(t) = 1+v(1--v)... and h = b/a. And we also obtain a new Young type inequality. Furthermore, corresponding operator inequalities are also established. [ABSTRACT FROM AUTHOR]