Approximation by Bivariate Bernstein-Kantorovich Operators that Reproduce Exponential Functions

Abstract

In this study, we construct bivariate Bernstein-Kantorovich polynomials which reproduce exponential function and investigate some approximation results for these operators. We use the test functions to prove Korovkin-type theorem. Thenweobtain the rate of convergence by means of the modulus of continuity. We demonstrate the Voronovskaya-type theorem for the newly constructed operator. In the last section, we represent some illustrative graphics to show the convergence of the constructed operators and we give some numerical results.