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Convergence properties of new \(\alpha \)-Bernstein–Kantorovich type operators

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Abstract

In the present paper, we introduce a new sequence of \(\alpha -\)Bernstein-Kantorovich type operators, which fix constant and preserve Korovkin’s other test functions in a limiting sense. We extend the natural Korovkin and Voronovskaja type results into a sequence of probability measure spaces. Then, we establish the convergence properties of these operators using the Ditzian-Totik modulus of smoothness for Lipschitz-type space and functions with derivatives of bounded variations.

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Acknowledgements

The second author is thankful to the Council of Scientific and Industrial Research (CSIR), India, Grant Code:-09/1217(0083)/2020-EMR-I for the financial support to pursue his research work.

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Authors and Affiliations

  1. Department of Mathematics, Bherulal Patidar Govt. P. G. College MHOW, Indore, Madhya Pradesh, 453441, India

    Ajay Kumar

  2. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, 221005, India

    Abhishek Senapati & Tanmoy Som

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  1. Ajay Kumar
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  2. Abhishek Senapati
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Correspondence to Abhishek Senapati.

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Communicated by Jaydeb Sarkar.

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Kumar, A., Senapati, A. & Som, T. Convergence properties of new \(\alpha \)-Bernstein–Kantorovich type operators. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00577-5

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