Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:71 Issue:2
Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$

Pages : 407-421

View : 15 | Download : 9

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ ∈ [ − 1 , 1 ] λ∈[−1,1] . Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre`s K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.
Keywords : Modulus of continuity, Lipschitz type class, Voronovskaya type asymptotic theorem, Szasz Mirakjan Durrmeyer operators, weighted approximation

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