Abstract
In this paper, we focus on pointwise and weighted approximation properties of newly defined Stancu variant of \( \lambda \)-Schurer operators. We establish a direct local approximation theorem and obtain a global approximation formula. These newly defined operators reduce to classical Schurer, Bernstein, Stancu, \( \lambda \)-Bernstein, \( \lambda \)-Stancu, \( \lambda \)-Schurer operators for the special cases of parameters. Certain illustrative and numerical examples are given to verify the convergence behavior and accuracy of the proposed operators. The numerical evaluations that obtained in this study may facilitate understanding and interpreting main results of this paper for the reader.
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Acknowledgements
The authors would like to express their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under Grant number R.G.P.2/172/42. Also, the authors would like to thank to the anonymous referees for their valuable comments and contributions.
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FÖ: writing—original draft preparation (lead), review and editing (equal). KJA: writing—review and editing (equal). ZÖÖ: software (lead), visualization (lead), review and editing (equal).
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Communicated by Yimin Wei.
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Ansari, K.J., Özger, F. & Ödemiş Özger, Z. Numerical and theoretical approximation results for Schurer–Stancu operators with shape parameter \( \lambda \). Comp. Appl. Math. 41, 181 (2022). https://doi.org/10.1007/s40314-022-01877-4
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DOI: https://doi.org/10.1007/s40314-022-01877-4
Keywords
- Shape parameter
- Pointwise convergence
- Weighted approximation
- Error estimation
- Computer graphics
- Numerical comparisons