Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
389138 | Fuzzy Sets and Systems | 2016 | 11 Pages |
Abstract
We prove that a family of continuous linear operators from a fuzzy quasi-normed space of the half second category to a fuzzy quasi-normed space is uniformly fuzzy bounded if and only if it is pointwise fuzzy bounded. This result generalizes and unifies several well-known results; in fact, the classical uniform boundedness principle, or Banach–Steinhauss theorem, is deduced as a particular case. Furthermore, we establish the relationship between uniform fuzzy boundedness and equicontinuity which allows us to give a uniform boundedness theorem in the class of paratopological vector spaces. The classical result for topological vector spaces is deduced as a corollary.
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Physical Sciences and Engineering
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Artificial Intelligence
Authors
Carmen Alegre, Salvador Romaguera,