Abstract
This paper deals with some approximation properties of Stancu-Kantorovich variant of Sz\'{a}sz-Mirakjan operators based on B\'{e}zier basis functions with shape parameter $\lambda\in\lbrack-1,1]$. We compute several preliminary results such as moments and central moments. Later, we introduce a Korovkin-type convergence theorem and discuss the order of approximation in terms of the modulus of continuity and for the elements belong to Lipschitz-type class and Peetre's $K$-functional, respectively. Also, we prove a Voronovskaya type asymptotic theorem. Lastly, we present the comparison of the convergence of constructed operators to the certain functions with some graphical illustrations for different values of $m$, $\alpha$, $\beta$ and $\lambda$ parameters.
Version Information
The current pdf replaces the original pdf file, first available on 5 April 2022. The new version corrects the DOI prefix to read 10.32513.
Citation
Resat Aslan. "On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter $\lambda$." Adv. Studies: Euro-Tbilisi Math. J. 15 (1) 151 - 166, March 2022. https://doi.org/10.32513/asetmj/19322008210
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