Approximation by bivariate Bernstein–Kantorovich–Stancu operators that reproduce exponential functions

Abstract

Abstract In this study, we construct a Stancu-type generalization of bivariate Bernstein–Kantorovich operators that reproduce exponential functions. Then, we investigate some approximation results for these operators. We use test functions to prove a Korovkin-type convergence theorem. Then, we show the rate of convergence by the modulus of continuity and give a Voronovskaya-type theorem. We give a covergence comparison about bivariate Bernstein–Kantorovich–Stancu operators and their exponential form.

Keywords

• Bernstein–Kantorovich–Stancu operators
• Modulus of continuity
• Bivariate operators
• Voronovskaya-type theorem