On the composite Bernstein type cubature formula

Considering a given function f ∈ C([0, 1] × [0, 1]), the bivariate interval [0, 1] × [0, 1] is divided in mn equally spaced bivariate subintervals k−1 m , k m × j−1 n , j n , k = 1, m, j = 1, n. On each such type of subinter-vals the Bernstein bivariate approximation formula is applied and a corresponding Bernstein type cubature formula is obtained. Making the sum of mentioned cubature formulas, the composite Bernstein type cubature formula is obtained. The coefficients of above formula are determined and an upper-bound for its remainder term is given.