Lacunary statistical convergence defined by an Orlicz function in sequences of fuzzy numbers

Article type: Research Article

Authors: Altinok, Hifsi^* | Yağdiran, Damla

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

Correspondence: [*] Corresponding author. Hifsi Altinok, Department of Mathematics, Fırat University, 23119 Elazığ, Turkey. Tel.: +90 4242370000; Fax: +90 4242330062; E-mail: [email protected].

Abstract: In the present paper, we introduce the concept of strongly Nθβ(p,F,Δm,M)-summable with respect to the Orlicz function M and examine the notions Sθβ(F,Δm)-statistical convergence and strong Nθβ(p,F,Δm,M)-summability for different two lacunary sequences and β ∈ (0, 1] . Moreover, we show that a sequence is Sθβ(F,Δm)-statistically convergent if it is strongly Nθ∣γ(p,F,Δm,M)-summable, where θ ={ kr } and θ′ ={ sr } are two lacunary sequences and give some inclusion relations between them.

Keywords: Sequence of fuzzy numbers, statistical convergence, lacunary sequence, difference sequence, Orlicz function

DOI: 10.3233/JIFS-16842

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2725-2731, 2017