Average quadrature formulas of Gauss type

In the average quadrature formulas the values of a given functionat given points are replaced by its averages over some distinctintervals. If all the intervals are of the same length, thequadrature formulas of interpolatory type and in particular,of Newton-Cotes type were constructed in Omladi (1978). Here,we construct average quadrature formulas of Gauss type for intervalsof the same length. The middle points of the intervals are zerosof polynomials, orthogonal in a technical sense.