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In this article we construct Bezier surfaces on a domain bounded by an astroid using the univariate polynomial Bernstein operator. We study the monotonicity and we give conditions of convexity in some directions for the constructed surfaces. Also, we give conditions for obtaining hyperbolic, parabolic and elliptic surfaces.

Mathematics Subject Classification (2010): 65D10, 41A10.

Keywords: Bezier surfaces, monotonicity, convexity.