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On Modulated Lacunary Statistical Convergence of Double Sequences

Author

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  • María del Pilar Romero de la Rosa

    (Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera, Cádiz, Spain)

Abstract

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for lacunary compatible modulus functions . Thus, we continue the work of Hacer Şenül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them.

Suggested Citation

  • María del Pilar Romero de la Rosa, 2023. "On Modulated Lacunary Statistical Convergence of Double Sequences," Mathematics, MDPI, vol. 11(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1042-:d:1072869
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    References listed on IDEAS

    as
    1. Fernando León-Saavedra & María del Pilar Romero de la Rosa & Antonio Sala, 2019. "Orlicz–Pettis Theorem through Summability Methods," Mathematics, MDPI, vol. 7(10), pages 1-5, September.
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    1. Fernando León-Saavedra & María del Pilar Romero de la Rosa & Antonio Sala, 2020. "Schur Lemma and Uniform Convergence of Series through Convergence Methods," Mathematics, MDPI, vol. 8(10), pages 1-11, October.

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