An Ostrowski type inequality is developed for estimating the
deviation of the integral mean of an absolutely continuous function, and
the linear combination of its values at k + 1 partition points, on a segment
of (real) linear spaces. Several particular cases are provided which
recapture some earlier results, along with the results for trapezoidal type
inequalities and the classical Ostrowski inequality. Some inequalities are
obtained by applying these results for semi-inner products; and some of
these inequalities are proven to be sharp.