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Approximation by the Parametric Generalization of Baskakov–Kantorovich Operators Linking with Stancu Operators

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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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Authors and Affiliations

  1. Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine

  2. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine & Abdullah Alotaibi

  3. Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia

    Naeem Ahmad

  4. Department of Engineering Sciences, İzmir Katip Çelebi University, 35620, İzmir, Turkey

    Faruk Özger

  5. Department of Mathematics, Gauhati University, Guwahati, 781014, Assam, India

    Bipan Hazarika

Authors
  1. S. A. Mohiuddine
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  2. Naeem Ahmad
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  3. Faruk Özger
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  4. Abdullah Alotaibi
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  5. Bipan Hazarika
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The authors contributed equally and significantly in writing this paper.

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Correspondence to S. A. Mohiuddine.

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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

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