On $\lambda$-weak convergence of sequences defined by an Orlicz function

Ömer Kişi^a, Mehmet Gurdal<sup>b

a</sup> Bartin University
^b Suleyman Demirel University, Kaskelen, Almaty

Abstract: In this article, we introduce and rigorously analyze the concept of difference $\lambda$-weak convergence for sequences defined by an Orlicz function. This notion generalizes the classical weak convergence by incorporating a $\lambda$-density framework and an Orlicz function, providing a more flexible tool for analyzing convergence behavior in sequence spaces. We systematically investigate the algebraic and topological properties of these newly defined sequence spaces, establishing that they form linear and normed spaces under suitable conditions. Our results include demonstrating the convexity of these spaces and identifying several important inclusion relationships among them, such as strict inclusions between spaces involving different orders of difference operators and Orlicz functions satisfying the $\Delta _{2}$-condition.

Keywords: Weak convergence, Orlicz function, $\lambda$ convergence.

Language: English

DOI: 10.15826/umj.2025.1.006

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