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

Laxmi Rathour|Resat Aslan
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2022.09|한국수학논문집 (Korean Journal of Mathematics)|제30권 제3호|pp. 539-553

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참고문헌

키워드

Lipschitz-type classSz'{a}sz-Mirakjan-Durrmeyer operatorsWeighted approximationPeetre's $K$-functionalVoronovskaya type asymptotic theorem.
주제분류수학

초록

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.

Abstract

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.

참고문헌 (45)

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