An Ostrowski type inequality for general convex functions defined
on linear spaces is generalised. Some inequalities which improve the Hermite-
Hadamard type inequality for convex functions defined on linear spaces are
derived using the obtained result. The results in normed linear spaces are
used to obtain some inequalities which are related to the given norm and
associated semi-inner products, and prove the sharpness of the constants in
those inequalities.