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Abstract

The main purpose of this work is to introducesome types of fuzzy convergence sequencesof operators defined on a standard fuzzy normed space(SFN-spaces) and investigate some properties and relationships between these concepts.Firstly,the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functionalis given. Then thenotionsof weakly andstrongly fuzzy convergence sequencesof operators (Γn)are introducedand essential theorems related to these conceptsare proved.In particular,if (Γn) is a strongly fuzzy convergent sequencewith a limit Γwhere Γlinear operatorfrom complete standard fuzzy normed space (U,��U,⊛)into a standard fuzzy normed space (V,��V,⊛)then Γbelongs to the set of all fuzzy bounded linear operators����(U,V). Furthermore, the concept of a fuzzy compact linear operatorin a standard fuzzy normed spaceis introduced. Also,several fundamental theoremsof fuzzy compact linear operators are studied in the samespace.More accurately, every fuzzy compact linear operatorΓ:U→Visproved to befuzzy boundedwhere (U,��U,⊛)and (V,��V,⊛)are two standard fuzzy normed spaces.

Keywords

Fuzzy compact linear operator, Fuzzy convergence sequence of operators, Standard fuzzy normed spaces, Strongly fuzzy convergent, Weakly fuzzy convergent

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