On approximation Bernstein-Chlodowsky-Gadjiev type operators preserve e^(-2x)

In this manuscript, we generalize the Bernstein-Chlodowsky-Gadjiev type operators which fix the function e^(-2x) for x ≥ 0. Then we provide the approximation properties of this newly defined operators for different type function spaces and rate of convergence. Additionally, we focus on the rate of convergence utilizing appropriate modulus of continuity. In addition to these, we provide the Voronovskaya type theorem for this new operators. Finally, in order to validate our theoretical results, we provide the numerical experiments which produced by MATLAB compiler.