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
Highlights
Fuzzy set theory was initiated by Zadeh in1965(1), numerous mathematicians have studied this concept and obtained different main results from various points of view[2,3]
Thought of a fuzzy normed linear space and the fuzzy linear operator was introduced by Shih Chuan and John Mordeson [6]
Bag and Samanta [7] studied the relation between fuzzy boundedness and fuzzy continuity and gave a notion of boundedness of a linear operator in fuzzy normed spaces. They debated the notions of convergent sequence and Cauchy sequence in the same space
Summary
1965(1), numerous mathematicians have studied this concept and obtained different main results from various points of view[2,3]. Bag and Samanta [7] studied the relation between fuzzy boundedness and fuzzy continuity and gave a notion of boundedness of a linear operator in fuzzy normed spaces. The first main goal is to present the definition of weak and strong fuzzy convergence sequence of operators in a standard fuzzy normed space This paper involves the following: the basic properties of a standard fuzzy normed space are given, in Section 3, the definition of strongly and weakly fuzzy convergence sequence of operators in an SFN-space are presented. We present some definitions of standard fuzzy normed spaces and basic properties related to these concepts. Is compact if and only if each sequence of elements in has a subsequence converging to an element in
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