On generalized integral Bernstein operators based on q-integers

The purpose of this paper is to study a simple integral generalization of q-analog of well known Bernstein operators with two parameters α and β, which was introduced in Mishra and Patel (2013) [17]. We give detail proof of the rate of convergence and Voronovskaja type asymptotic formula for the operators Dn,qα,β. Also, we establish statistical convergence for these operators and discuss modification of the operators Dn,qα,β for better approximation results over compact interval.