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

Year 2022, Volume: 71 Issue: 2, 407 - 421, 30.06.2022

Reşat Aslan

https://doi.org/10.31801/cfsuasmas.941919

Cited By: 11

Abstract

In this
paper, we study several approximation properties of
Szasz-Mirakjan-Durrmeyer operators with shape parameter $\lambda \in [-1,1]$. 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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