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A new approach to Korovkin-type approximation via deferred Cesàro statistical measurable convergence

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  • Jena, Bidu Bhusan
  • Paikray, Susanta Kumar
  • Dutta, Hemen

Abstract

The work of this paper aims to introduce the notions of statistical mean convergence, statistical measurable convergence, and statistical Lebesgue measurable convergence by means of deferred Cesàro summability and apply them in Korovkin-type new approximations. We first established some fundamental results to understand the connections among them. Then we established new versions of Korovkin-type theorems with three algebraic test functions via deferred Cesàro statistical Lebesgue measurable convergence for sequences of measurable functions. Also, several examples have been given in the sequel to support our new ideas and findings.

Suggested Citation

  • Jena, Bidu Bhusan & Paikray, Susanta Kumar & Dutta, Hemen, 2021. "A new approach to Korovkin-type approximation via deferred Cesàro statistical measurable convergence," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
  • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003702
    DOI: 10.1016/j.chaos.2021.111016
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    References listed on IDEAS

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    1. 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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