Lacunary statistical convergence on L- fuzzy normed space

Article type: Research Article

Authors: Yapali, Reha^{a; *} | Korkmaz, Erdal^a | Çinar, Muhammed^a | Çoskun, Hüsamettin^b

Affiliations: [a] Mathematics Department, Mus Alparslan University, Turkey | [b] Mathematics Department, Manisa Celal Bayar University

Correspondence: [*] Corresponding author. Reha YAPALI, Mus Alparslan University, Mathematics Department, Turkey. E-mail: [email protected].

Abstract: The idea of lacunary statistical convergence sequences, which is a development of statistical convergence, is examined and expanded in this study on L- fuzzy normed spaces, which is a generalization of fuzzy spaces. On L- fuzzy normed spaces, the definitions of lacunary statistical Cauchy and completeness, as well as associated theorems, are provided. The link between lacunary statistical Cauchyness and lacunary statistical boundedness with regard to L- fuzzy norm is also shown.

Keywords: ℒ-fuzzy normed space, lacunary double sequences, lacunary statistically convergence, lacunary statistical Cauchy, lacunary statistical boundedness

DOI: 10.3233/JIFS-222695

Journal: Journal of Intelligent & Fuzzy Systems, vol. 46, no. 1, pp. 1985-1993, 2024