Abstract
We define the summation-integral-type operators involving the ideas of Polya-Eggenberger distribution and Bezier basis functions, and study some of their basic approximation properties. In addition, by means of the Ditzian-Totik modulus of smoothness, we study a direct theorem as well as a quantitative Voronovskaja-type theorem for our newly constructed operators. Moreover, we investigate the approximation of functions with derivatives of bounded variation (DBV) of the aforesaid operators.