A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces

Year 2025, Volume: 13 Issue: 4, 179 - 189

Hafize Gumus , Seyma Bolat

https://doi.org/10.36753/mathenot.1720763

Abstract

Following the studies on gradual numbers, which are expressed with membership functions and have many important application areas in daily life, studies on gradual normed linear spaces (GNLS) have also gained speed in recent years. On the other hand, it is thought that the definition of $\mathcal{I-}$statistical convergence, which generalizes many types of convergence, for a sequence in these spaces, and the results obtained will be important. For this reason, lacunary $\mathcal{I-}$statistical convergence in gradual normed linear spaces is defined in this paper. Therefore, more general results were obtained compared to previous studies in this area.

Keywords

$\mathcal{I-}$Convergence , $\mathcal{I-}$ statistical convergence , Gradual normed linear space , Gradual numbers , Lacunary sequences , Statistical convergence

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