Lacunary statistical convergence of order β in difference sequences of fuzzy numbers

Article type: Research Article

Authors: Altinok, Hifsi^* | Yagdiran, Damla

Affiliations: Department of Mathematics, Fırat University, Elazığ, Turkey

Correspondence: [*] Corresponding author. Hıfsı Altinok, Department of Mathematics, Fırat University, 23119, Elazığ, Turkey. Tel.: +904242370000; Fax: +904242330062; E-mail: hifsialtinok@yahoo.com.

Abstract: In this paper, we define the spaces Nθβ(p,F,Δm), Sθβ(F,Δm), wpβ(F,Δm) for sequences of fuzzy numbers using generalized difference operator Δm and a lacunary sequence θ and give some relations between them, where β ∈ (0, 1] and p > 0. Furthermore, in the last section of paper, some inclusion theorems are presented related to the spaces Sθβ(F,Δm) and wpβ(θ,f,F,Δm) according to modulus function f.

Keywords: Fuzzy number, sequence of fuzzy numbers, statistical convergence, lacunary sequence, Cesàro summability, modulus function

DOI: 10.3233/IFS-162136

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 1, pp. 227-235, 2016