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Double lacunary statistical convergence of Δ-measurable functions on product time scales

  • Hemen Dutta EMAIL logo and Pallav Bhattarai
Published/Copyright: October 4, 2023
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Abstract

We first present a notion of a double lacunary sequence on product time scales. Using this notion, we define the notions of the double lacunary statistical convergence and double lacunary strongly p-Cesàro summability of 2-multiple functions on product time scales and we study some fundamental properties of both notions. We also present a theorem that connects the above-mentioned two concepts. Furthermore, we define a refinement of a double lacunary sequence on product time scales and provide some fundamental properties as well as inclusion theorems for a refined and a non-refined double lacunary sequence on product time scales.

MSC 2020: 40A35; 40B05; 26E70

Acknowledgements

We are thankful to the referees for their valuable comments and suggestions.

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Received: 2023-03-02
Revised: 2023-04-04
Accepted: 2023-04-11
Published Online: 2023-10-04
Published in Print: 2024-04-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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