We consider a sequence of composite bivariate Bernstein operators and the cubature formula associated with them. The upper bounds for the remainder term of a cubature formula are described in terms of moduli of continuity of order two. Also, we include some results showing how nonmultiplicative the integration functional is.
"Composite Bernstein cubature." Banach J. Math. Anal. 10 (2) 235 - 250, April 2016. https://doi.org/10.1215/17358787-3492611