Abstract
In this paper, we define three types of fuzzy n-continuous linear operators (strongly, weakly, and sequentially) and research the relation between three. Also strongly, weakly fuzzy n-bounded linear operators and the closed graph theorem are defined. https://doi.org/10.28919/jmcs/3428
Highlights
In 1984, Katsaras [4] introduced the concept of fuzzy norm
In 1992, Felbin [5] introduced an idea of fuzzy norm on a linear space by assigning a fuzzy real number to each element of the linear space, so that corresponding metric associated to this fuzzy norm is a Kaleva type fuzzy metric
In 2005, Narayanan and Vijayabalaji [6] extended the notion of n-normed linear space to fuzzy n-normed linear space
Summary
In 1992, Felbin [5] introduced an idea of fuzzy norm on a linear space by assigning a fuzzy real number to each element of the linear space, so that corresponding metric associated to this fuzzy norm is a Kaleva type fuzzy metric. In 2005, Narayanan and Vijayabalaji [6] extended the notion of n-normed linear space to fuzzy n-normed linear space. In2012, A.L.Soenjaya [9] defined n-bounded and n-continuous linear operators in n-normed linear space. Defined two types of fuzzy 2-bounded linear operators. We extend the notion of three types of fuzzy n-continuous linear operators (strongly, weakly, and sequentially) and research the relation between three. Strongly , weakly fuzzy n-bounded linear operators and the closed graph theorem are defined
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