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Common fixed point results for single and multivalued maps in fuzzy metric spaces using countable extension of \(t\)-norms. (English) Zbl 1374.54045

Summary: The aim of this paper is to prove some common fixed point theorem for four single-valued mappings in complete fuzzy metric spaces and a common fixed point theorem for single-valued mappings \(I,J:X\to X\) and multi-valued mappings \(F,G:X\to CB(X)\) using an implicit relation. It is shown that the theorems can be applied to a wide class of \(t\)-norms using the theory of the countable extensions given in O. Hadžić and E. Pap [Fixed point theory in probabilistic metric spaces. Dordrecht: Kluwer Academic Publishers (2002; Zbl 0994.47077)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54A40 Fuzzy topology
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E50 Complete metric spaces
54C60 Set-valued maps in general topology

Citations:

Zbl 0994.47077
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