Approximation properties of rth order generalized Bernstein polynomials based on q-calculus

Abstract

In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre’s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.