Approximation theorems for Kantorovich type Lupaș-Stancu operators based on \(q\)-integers

Abstract

In this paper, we introduce a Kantorovich generalization of q-Stancu-Lupa¸s operators and investigate their approximation properties. The rate of convergence of these operators are obtained by means of modulus of continuity, functions of Lipschitz class and Peetre's K-functional. We also investigate the convergence of the operators in the statistical sense and give a numerical example in order to estimate the error in the approximation.

Keywords

• Lupas-Kantorovich operators
• modulus of continuity
• Peetre's K-functional
• q-integers
• rate of convergence
• statistical approximation