Year: 2025
Type: article
Abstract: This paper explores the notions of lacunary $ \Delta^m $-statistical convergence, lacunary $ \Delta^m $-statistical Cauchy sequences, and lacunary strongly $ \Delta^m $-convergence within the framework of neutrosophic normed linear spaces (NNLS). We establish the uniqueness of limit and certain algebraic properties of lacunary $ \Delta^m $-statistical convergence in NNLS, offering a rigorous foundation for these concepts. Additionally, we introduce the concept of strong Cesàro summability in NNLS and conduct an in-depth analysis of its properties. The connections between lacunary strong $ \Delta^m $-convergence and Cesàro summability are also examined, revealing significant interrelationships between these two convergence methods.
DOI: 10.3934/mfc.2025023
Institutions: Malatya Turgut Özal Üniversitesi, Turgut Özal University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411782291