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The aim of this paper is to provide some results on Bernstein quasi-interpolants of different types applied to functions defined on a triangle. Classical multivariate Bernstein operators and their extensions have been studied for about 25 years by various authors. Based on their representation as differential operators, we extend our previous results on the univariate case to the multivariate one and we define new families of Bernstein quasi-interpolants. Then we compare their approximation properties on various types of functions. Our approach seems to be distinct from another interesting extension given in [5, 6].

Mathematics Subject Classification (2010): 41A35, 41A63.

Keywords: Bernstein operators.