A Kantorovich type integral modification of q-Bernstein-Schurer operators

Abstract

The q-Bernstein-Schurer summation type operators are modified in order to make them applicable for approximation of integrable functions. The aim of the paper is twofold. Firstly, to find refined error estimates, |S*(?,?) n,p,q(f)(x) - f(x)| without using Schwarz?s inequality. Secondly, to obtain a generalized Voronovskaya type asymptotic formula. The rate of approximation in terms of modulus of smoothness are also established.