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

Bidu Bhusan Jena, Susanta Kumar Paikray and Hemen Dutta

Chaos, Solitons & Fractals, 2021, vol. 148, issue C

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.

Keywords: Measurable convergence; Mean convergence; Deferred Cesàro statistical measurable convergence; Deferred Cesàro statistical Lebesgue measurable convergence; Korovkin-type theorem (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003702

DOI: 10.1016/j.chaos.2021.111016

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