Abstract
In this paper we introduce and study some new sequence spaces of fuzzy numbers defined by I-convergence using the sequences of Orlicz functions, infinite matrix. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces.
Highlights
The theory of sequence of fuzzy numbers was first introduced by Matloka [10]
Nanda [12] studied the sequence of fuzzy numbers and showed that the set of all convergent sequence of fuzzy numbers forms a complete metric space
Mursaleen and Basarir [11] introduced and studied some new sequence space of fuzzy numbers generated by non-negative regular matrix
Summary
The theory of sequence of fuzzy numbers was first introduced by Matloka [10]. Matloka introduced bounded and convergent sequence of fuzzy numbers and studied some of their properties and showed that every convergent sequence of fuzzy numbers is bounded. Nanda [12] studied the sequence of fuzzy numbers and showed that the set of all convergent sequence of fuzzy numbers forms a complete metric space. Savas [17] introduced and discussed double convergent sequence of fuzzy numbers and showed that the set of all double convergent sequence of fuzzy numbers is complete. We study some new sequence spaces of fuzzy numbers defined by using I-convergence, the sequence of Orlicz functions and an infinite matrix. We establish inclusion relations between the sequence spaces wI(F) A, M, p , wI(F) A, M , p 0 , wF A, M , p and wI(F) A, M , p where p=(pk) denote the sequence of positive real numbers for all n N and M=(Mk) be a sequence of Orlicz functions
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