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Convergence of \(\lambda \)-Bernstein operators via power series summability method

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Abstract

In this paper we present uniform convergence of a sequence of \(\lambda \) -Bernstein operators via A-statistical convergence and power summability method. A rate of convergence of the sequence of operators are also investigated by means of above mentioned summability methods. The last section is devoted to pointwise convergence (A-statistical convergence) of the sequence of operators in terms of Voronovskaya and Grü ss–Voronovskaya type theorems.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Prishtina, Avenue Mother Teresa, No-5, 10000, Pristina, Kosova

    Naim L. Braha

  2. Research Institute Ilirias, Rr-Janina No-2, Ferizaj, 70000, Kosovo

    Naim L. Braha

  3. Department of Mathematics, University of Haifa, 3498838, Haifa, Israel

    Toufik Mansour

  4. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

    M. Mursaleen

  5. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen

  6. Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

    M. Mursaleen

  7. Department of Mathematics, Selcuk University, 42003, Konya, Turkey

    Tuncer Acar

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  1. Naim L. Braha
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  2. Toufik Mansour
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  3. M. Mursaleen
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  4. Tuncer Acar
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Correspondence to M. Mursaleen.

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Braha, N.L., Mansour, T., Mursaleen, M. et al. Convergence of \(\lambda \)-Bernstein operators via power series summability method. J. Appl. Math. Comput. 65, 125–146 (2021). https://doi.org/10.1007/s12190-020-01384-x

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  • DOI: https://doi.org/10.1007/s12190-020-01384-x

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