Lacunary Statistically Convergence via Modulus Function Sequences

Year 2024, Volume: 12 Issue: 4, 187 - 195, 08.12.2024

Erdal Bayram , Çiğdem Bektaş

https://doi.org/10.36753/mathenot.1477450

Abstract

Modifying the definition of density functions is one method used to generalise statistical convergence. In the present study, we use sequences of modulus functions and order $\alpha \in \left( 0,1\right] $ to introduce a new density. Based on this density framework, we define strong $(f_k)$-lacunary summability of order $\alpha $ and $(f_k)$-lacunary statistical convergence of order $\alpha $ for a sequence of modulus functions $(f_k)$. This concept holds an intermediate position between the usual convergence and the statistical convergence for lacunary sequences. We also establish inclusion theorems and relations between these two concepts in the study.

Keywords

Lacunary statistical convergence, Lacunary summability, Modulus function, Weighted density

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