Abstract
In this paper, spaces of sequences in fuzzy normed spaces are considered. These spaces are a new concept in fuzzy normed spaces. We develop fuzzy norms for spaces of sequences in fuzzy normed spaces. Especially, we study the representation of the dual of a space of sequences in a fuzzy normed space. The approximation property in our context is investigated.
Highlights
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We study spaces of sequences in fuzzy normed spaces
We provide the representation of strong fuzzy dual space of space of null sequence in fuzzy normed spaces
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Many researchers concentrated on investigating the convergency of sequences in fuzzy normed spaces and their topological properties. We establish a well-defined fuzzy norm for spaces of sequences in fuzzy normed spaces and its completeness This is an important contribution of our paper. The contribution of our paper is to make tools for fuzzy analysis, because we characterize the duality and approximation property in the sense of sequences in fuzzy normed spaces. We provide their completeness and several examples.
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