Felbin模糊赋范线性空间上一类模糊有界算子和模糊度量空间中的不动点定理

发布时间：2018-03-24 19:24

本文选题：模糊赋范线性空间　切入点：模糊范数　出处：《青岛大学》2017年硕士论文

【摘要】：本文首先提出了Felbin模糊赋范线性空间上一类模糊有界算子的模糊范数的定义,指出了此类模糊有界算子构成模糊赋范线性空间,研究了此空间赋此模糊范数的拓扑结构和完备性。然后,在模糊度量空间中引入了广义(Φ,ψ) -弱压缩映射的概念,推广了文献[20]在度量空间中提出的(Φ,ψ) -弱压缩映射的概念,并证明了相应的不动点的存在性和唯一性。最后,本文考虑了模糊度量空间中的一类模糊循环压缩映射和循环广义φ-压缩映射,证明了满足压缩条件的不动点定理,推广了文献[22]和文献[24]的结论。
[Abstract]:In this paper, the definition of fuzzy norm of a class of fuzzy bounded operators on Felbin fuzzy normed linear spaces is proposed, and it is pointed out that this kind of fuzzy bounded operators constitute fuzzy normed linear spaces. In this paper, the topological structure and completeness of fuzzy norm in this space are studied. Then, the concept of generalized (桅, 蠄) -weakly contractive mapping in fuzzy metric space is introduced, and the concept of (桅, 蠄) -weakly contractive mapping proposed in [20] in metric space is generalized. The existence and uniqueness of the corresponding fixed points are proved. Finally, a class of fuzzy cyclic contractive mappings and cyclic generalized 蠁 -contractive mappings in fuzzy metric spaces are considered, and the fixed point theorems satisfying the contraction conditions are proved. The conclusions of [22] and [24] are generalized.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177

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