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, $|\mathbb{S}_{n,p,q}^{*(\alpha,\beta)}(f)(x)-f(x)|$ 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.