  Some extremalities for quadrature operators are proved for convex functions
of higher order. Such results are known in the numerical analysis, however they
are often proved under suitable differentiability assumptions. In our
considerations we do not use any other assumptions apart from higher order
convexity itself. The obtained inequalities refine the inequalities of Hadamard
type. They are applied to give error bounds of quadrature operators under the
assumptions weaker from the commonly used.
