Abstract: | We establish inequalities of the following form. If f C(1)[a,b], and x [a,b], then where (f') = max f' – min f'. Moreover, it is impossible to decrease the sum of constants at the norm and half oscillation on the right-hand side of the inequality. We cannot decrease the constant at the norm even if we increase the constant at the oscillation. This inequality implies the known sharp Ostrowski inequality. Bibliography: 7 titles. |