Some types of convergence in gradual 2-normed spaces

This study focuses on investigating gradual statistical convergence in the context of gradual 2-normed linear spaces (G2NLS). Our research demonstrates that certain properties related to gradual statistical convergence of real number sequences extend to sequences within G2NLS. Additionally, we introduce the concept of gradual statistical Cauchy sequences in G2NLS and establish criteria for characterizing a sequence as a gradual statistical Cauchy sequence in such spaces. This research contributes to a deeper understanding of gradual statistical convergence in the G2NLS framework and elucidates its mathematical applicability and unique characteristics. The study explores the concept of gradual J-convergence normed spaces, introduces and examines new sequence spaces using the gradual 2-norm. Furthermore, it addresses the concepts of gradual J-convergence and gradual J-Cauchy sequences within G2NLS, investigates their interrelationships, and presents significant findings regarding these classes.