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Approximation via equi-statistical convergence in the sense of power series method

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this study, we define a new type of convergence using the notions of statistical convergence in the sense of the power series method and equi-statistical convergence then, we give an example that supports this new definition and after that we use it to prove a Korovkin-type approximation theorem. This theorem is a non-trivial generalization of Korovkin-type approximation theorems that have been studied in earlier papers. Also, we present an example that satisfies our approximation theorem which hasn’t satisfied the one studied before. Moreover, we calculate the rate of equi-statistical convergence in the sense of the power series method and then, we prove a Voronovskaya-type approximation theorem. Finally, we summarize our results in the conclusion section.

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Authors and Affiliations

  1. Department of Mathematics, Sinop University, Sinop, Turkey

    Kamil Demirci, Fadime Dirik & Sevda Yıldız

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  1. Kamil Demirci
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  2. Fadime Dirik
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  3. Sevda Yıldız
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Correspondence to Fadime Dirik.

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Demirci, K., Dirik, F. & Yıldız, S. Approximation via equi-statistical convergence in the sense of power series method. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 65 (2022). https://doi.org/10.1007/s13398-021-01191-4

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  • DOI: https://doi.org/10.1007/s13398-021-01191-4

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