本文選題：模糊賦范線性空間　切入點(diǎn)：模糊范數(shù)　出處：《青島大學(xué)》2017年碩士論文

【摘要】：本文首先提出了Felbin模糊賦范線性空間上一類模糊有界算子的模糊范數(shù)的定義,指出了此類模糊有界算子構(gòu)成模糊賦范線性空間,研究了此空間賦此模糊范數(shù)的拓?fù)浣Y(jié)構(gòu)和完備性。然后,在模糊度量空間中引入了廣義(Φ,ψ) -弱壓縮映射的概念,推廣了文獻(xiàn)[20]在度量空間中提出的(Φ,ψ) -弱壓縮映射的概念,并證明了相應(yīng)的不動點(diǎn)的存在性和唯一性。最后,本文考慮了模糊度量空間中的一類模糊循環(huán)壓縮映射和循環(huán)廣義φ-壓縮映射,證明了滿足壓縮條件的不動點(diǎn)定理,推廣了文獻(xiàn)[22]和文獻(xiàn)[24]的結(jié)論。
[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.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O177

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 常曉璇;紀(jì)培勝;;Felbin模糊賦范線性空間上一類模糊有界算子[J];山東大學(xué)學(xué)報(理學(xué)版);2017年02期

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本文編號：1659692