On \(\lambda\)-ideal convergent interval valued difference classes defined by Musielak-Orlicz function. (English) Zbl 1315.46006
Summary: An ideal \(I\) is a family of subsets of positive integers \(\mathbb{N}\) which is closed under taking finite unions and subsets of its elements. In this paper, using \(\lambda\)-ideal convergence as a variant of the notion of ideal convergence, the difference operator \(\Delta^n\) and Musielak-Orlicz functions, we introduce and examine some generalized difference sequences of interval numbers, where \(\lambda=(\lambda_m)\) is a nondecreasing sequence of positive real numbers such that \(\lambda_{m+1}\leq\lambda_{m}+1\), \(\lambda_{1}=1\), \(\lambda_{m}\to\infty\) \((m\to\infty)\). We prove completeness properties of these spaces. Further, we investigate some inclusion relations related to these spaces.
MSC:
| 46A45 | Sequence spaces (including Köthe sequence spaces) |
| 40A35 | Ideal and statistical convergence |
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