Korean J. Math. Vol. 30 No. 3 (2022) pp.539-553
DOI: https://doi.org/10.11568/kjm.2022.30.3.539

On approximation properties of Stancu variant $\lambda$-Szász-Mirakjan-Durrmeyer operators

Main Article Content

Resat Aslan
Laxmi Rathour


In the present paper, we aim to obtain several approximation properties of Stancu form Sz\'{a}sz-Mirakjan-Durrmeyer operators based on B\'{e}zier basis functions with shape parameter $\lambda \in\lbrack-1,1]$. 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.

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