On fuzzy valued lacunary ideal convergent sequence spaces defined by a compact operator

Article type: Research Article

Authors: Khan, Vakeel A.^{; *} | Makharesh, Abdullah A.H. | Alshlool, Kamal M.A.S | Abdullah, Sameera A.A. | Fatima, Hira

Affiliations: Department of Mathematics, Aligarh Muslim University, Aligarh, India

Correspondence: [*] Corresponding author. Vakeel A. Khan, Department of Mathematics, Aligarh Muslim University, Aligarh, India. E-mail: [email protected].

Abstract: In this paper, our aim is to introduce and study some new spaces of lacunary I - convergence for sequence of fuzzy real number which are defined by compact operator (T) on the real space ℝ . i.e., cFIθ(T), cF0Iθ(T), ℓF∞Iθ(T), ℓF∞θ(T) and examine some basic properties and prove some inclusions relation on these spaces.

Keywords: Ideal, I_θ—convergence, I_θ—Cauchy, fuzzy number, lacunary sequence, compact operator

DOI: 10.3233/JIFS-18906

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4849-4855, 2018