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Korovkin theory via \(P_{p}-\)statistical relative modular convergence for double sequences

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Abstract

In this paper, we introduce a new type of statistical relative modular convergence for the first time and we obtain Korovkin theorems for double sequences of positive linear operators on modular spaces in the sense of this new statistical type convergence with respect to power series method. Finally, we present an interesting application that satisfies our new approximation theorem but not satisfies the classical ones. So, we show that our results are meaningful.

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Acknowledgements

We would like to thank the referees for reading carefully and making valuable suggestions.

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The authors have no received any financial support for the research, authorship, or publication of this study.

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Authors and Affiliations

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

    Sevda Yıldız, Kamil Demirci & Fadime Dirik

Authors
  1. Sevda Yıldız
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  2. Kamil Demirci
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  3. Fadime Dirik
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All authors have contributed sufficiently in the planning, execution, or analysis of this study to be included as authors. All authors read and approved the final manuscript.

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Correspondence to Sevda Yıldız.

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Yıldız, S., Demirci, K. & Dirik, F. Korovkin theory via \(P_{p}-\)statistical relative modular convergence for double sequences. Rend. Circ. Mat. Palermo, II. Ser 72, 1125–1141 (2023). https://doi.org/10.1007/s12215-021-00681-z

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  • DOI: https://doi.org/10.1007/s12215-021-00681-z

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