Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces

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Raghad I. Sabri

Abstract

The main purpose of this work is to introduce some types of fuzzy convergence sequences of 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 functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators . Furthermore, the concept of a fuzzy compact linear operator in a standard fuzzy normed space is introduced. Also, several fundamental theorems of fuzzy compact linear operators are studied in the same space. More accurately, every fuzzy compact linear operator  is proved to be fuzzy bounded  where  and  are two standard fuzzy normed spaces

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I. Sabri R. Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces. Baghdad Sci.J [Internet]. [cited 2021Aug.4];18(4):1204. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4693
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