Statistical Deferred Nörlund Summability and Korovkin-Type Approximation Theorem

Hari Mohan Srivastava, Bidu Bhusan Jena and Susanta Kumar Paikray
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Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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

Mathematics, 2020, vol. 8, issue 4, 1-11

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.

Keywords: statistical convergence; statistical deferred Nörlund summability; positive linear operators; sequences of real variables; banach space; korovkin-type approximation theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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