Abstract
In this paper, using the difference operator of order m, the sequences of Orlicz functions, and an infinite matrix, we introduce and examine some classes of sequences of fuzzy numbers defined by I-convergence. We study some basic topological and algebraic properties of these spaces. In addition, we shall establish inclusion theorems between these sequence spaces.MSC:40A05, 40G15, 46A45.
Highlights
1 Introduction The notion of ideal convergence was introduced first by Kostyrko et al [ ] as a generalization of statistical convergence [, ], which was further studied in topological spaces [ ]
We study some new sequence spaces of fuzzy numbers using I-convergence, the sequence of Orlicz functions, an infinite matrix, and the difference operator
3 Some new sequence spaces of fuzzy numbers using the sequence of Orlicz functions, an infinite matrix, the difference operator m, and I-convergence, we introduce the following new sequence spaces and examine some properties of the resulting sequence spaces
Summary
The notion of ideal convergence was introduced first by Kostyrko et al [ ] as a generalization of statistical convergence [ , ], which was further studied in topological spaces [ ]. Throughout the article, wF denotes the class of all fuzzy real-valued sequence spaces. We study some new sequence spaces of fuzzy numbers using I-convergence, the sequence of Orlicz functions, an infinite matrix, and the difference operator. We establish the inclusion relation between the sequence spaces wI(F)[A, M, m, p], wI(F)[A, M, m, p] , wF [A, M, m, p]∞, and wI(F)[A, M, m, p]∞, where p = (pk) denotes the sequence of positive real numbers for all k ∈ N and M = (Mk) is a sequence of Orlicz functions. Let p = (pk) be any sequence of positive real numbers with ≤ pk ≤ supk pk = G, H = max{ , G– }, . To prove that g(umk Xkm – uXk) → as m → ∞, let uk → u, where uk, u ∈ C and g(Xkm – Xk) → as m → ∞
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