Abstract
We construct the Baskakov–Kantorovich operators based on shape parameter \(\alpha\) by linking with Stancu operators to approximate functions over unbounded intervals. We establish local approximation results with the help of suitable modulus of continuity, \({\mathcal {K}}\)-functional and Lipschitz-type space. Further, we obtain the weighted approximation properties and calculate the rate of convergence with a view of weighted modulus of continuity of our newly defined operators. Moreover, we present several numerical results for viewing the convergence and illustrate the error of approximation of aforesaid operators.
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Acknowledgements
This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant No. (RG-36-130-38). The authors, therefore, acknowledge with thanks DSR for technical and financial support.
Funding
This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (RG-36-130-38).
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Mohiuddine, S.A., Ahmad, N., Özger, F. et al. Approximation by the Parametric Generalization of Baskakov–Kantorovich Operators Linking with Stancu Operators. Iran J Sci Technol Trans Sci 45, 593–605 (2021). https://doi.org/10.1007/s40995-020-01024-w
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DOI: https://doi.org/10.1007/s40995-020-01024-w
Keywords
- Baskakov operators
- \(\alpha\)-Baskakov–Kantorovich
- Modulus of continuity
- Rate of convergence
- Weighted approximation