ON APPROXIMATION PROPERTIES OF STANCU VARIANT λ-SZASZ-MIRAKJAN-DURRMEYER OPERATORS

In the present paper, we aim to obtain several approximation properties of Stancu form Szasz-Mirakjan-Durrmeyer operators based on Be ' zier basis functions with shape parameter lambda E [-1, 1]. We estimate some auxiliary results such as moments and central moments. Then, we obtain the order of convergence in terms of the Lipschitz-type class functions and Peetre's K-functional. Further, we prove weighted approximation theorem and also Voronovskaya-type asymptotic theorem. Finally, to see the accuracy and effectiveness of discussed operators, we present comparison of the convergence of constructed operators to certain functions with some graphical illustrations under certain parameters.