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Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem

Author

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  • Hari Mohan Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan)

  • Bidu Bhusan Jena

    (Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, India)

  • Susanta Kumar Paikray

    (Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, India)

Abstract

The concept of the deferred Nörlund equi-statistical convergence was introduced and studied by Srivastava et al. [Rev. Real Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. (RACSAM) 112 (2018), 1487–1501]. In the present paper, we have studied the notion of the deferred Nörlund statistical convergence and the statistical deferred Nörlund summability for sequences of real numbers defined over a Banach space. We have also established a theorem presenting a connection between these two interesting notions. Moreover, based upon our proposed methods, we have proved a new Korovkin-type approximation theorem with algebraic test functions for a sequence of real numbers on a Banach space and demonstrated that our theorem effectively extends and improves most of the earlier existing results (in classical and statistical versions). Finally, we have presented an example involving the generalized Meyer–König and Zeller operators of a real sequence demonstrating that our theorem is a stronger approach than its classical and statistical versions.

Suggested Citation

  • Hari Mohan Srivastava & Bidu Bhusan Jena & Susanta Kumar Paikray, 2020. "Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:636-:d:348365
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    References listed on IDEAS

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    1. Kadak, Uğur & Braha, Naim L. & Srivastava, H.M., 2017. "Statistical weighted B-summability and its applications to approximation theorems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 80-96.
    2. Braha, Naim L. & Loku, Valdete & Srivastava, H.M., 2015. "Λ2-Weighted statistical convergence and Korovkin and Voronovskaya type theorems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 675-686.
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