广义模糊赋范空间中的收敛性(英文)

Convergence in a generalized fuzzy normed space

目的证明广义模糊赋范空间中关于收敛的一些性质。方法定义了广义模糊赋范空间,模糊收敛性,模糊有界性,柯西列和完备性。借助这些定义,证明了广义模糊赋范空间中序列的若干收敛定理。而且考虑了这种完备性和赋范空间中的完备性的关系。结果证明了以下结果:模糊收敛序列的极限是唯一的;模糊收敛序列的任一子列模糊收敛到此序列的极限;模糊收敛的序列是柯西列;柯西列是模糊有界的;任一有模糊收敛子列的柯西列是模糊收敛的;存在不完备的广义模糊赋范空间。结论说明赋范空间中的一些概念和结果可类似的在广义模糊赋范空间中建立。

Aim To prove some properties about convergence in a generalized fuzzy normed space.Methods By introducing the definitions of generalized fuzzy normed space,fuzzy convergence,fuzzy boundedness,Cauchy sequence and completeness,several convergence theorems of sequences in a generalized fuzzy normed space are proved.Moreover the relation between this kind of completeness and completeness in a normed space is considered.Results The following results are obtained： limit of a fuzzy convergent sequence is unique;each subsequence of a fuzzy convergent sequence converges to the limit of the sequence;each fuzzy convergent sequence is a Cauchy sequence;each Cauchy sequence is fuzzy bounded and each Cauchy sequence which has a fuzzy convergent subsequence is fuzzy convergent and there exist incomplete generalized fuzzy normed spaces.Conclusion It has been shown that some concepts and results in a normed space can be similarly established in a generalized fuzzy normed space.