模糊距离空间中Meir-Keeler型不动点定理
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摘要
在Kaleva-Seikkala型模糊距离空间中建立Meir-Keeler型不动点定理.作为应用,给出了通常距离空间和Menger概率距离空间中的Meir-Keeler型不动点定理.
In the Kaleva-Seikkala type fuzzy metric spaces,a fixed point theorem of Meir-Keeler type is established.As applications of our results,Meir-Keeler type fixed point theorems in ordinary metric spaces and Menger probabilistic metric spaces are obtained.
In the Kaleva-Seikkala type fuzzy metric spaces,a fixed point theorem of Meir-Keeler type is established.As applications of our results,Meir-Keeler type fixed point theorems in ordinary metric spaces and Menger probabilistic metric spaces are obtained.
引文
[1]Kaleva O,Seikkala S.On fuzzy metric spaces[J].Fuzzy Sets Syst,1984,12:215-229.
[2]Hadzic O,Pap E.A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces[J].Fuzzy Sets Syst,2002,127:333-444.
[3]Hadzic O.Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces[J].Fuzzy Sets Syst,1989,29:115-125.
[4]Fang J X.A note on fixed point theorem of Hadzic[J].Fuzzy Sets Syst,1992,48:391-395.
[5]Xiao J Z,Zhu X H,Jin X.Fixed point theorem for nonlinear contractions in Kaleva-Seikkala’s type fuzzy metric spaces[J].Fuzzy Sets Syst,2012,200:65-83.
[6]Zhu J,Zhong C K,Wang G P.An extension of Ekeland’s variational principle in fuzzy metric spaces and its application[J].Fuzzy Sets Syst,1999,108:353-363.
[7]Jachymski J.Equivalent conditions and the Meir-Keeler type theorems[J].Math Anal Appl,1995,194:293-303.
[8]Boyd D W,Wong J S.On nonlinear contractions[J].Proc Am Math Soc,1969,20:458-464.
[9]Xiao J Z,Zhu X H.On linearly topological structure and property of fuzzy normed linear space[J].Fuzzy Sets Syst,2002,125:153-161.
[10]Xiao J Z,Zhu X H.Topological degree theory and fixed point theorems in fuzzy normed linear spaces[J].Fuzzy Sets Syst,2004,147:437-452.
[11]Alegre C,Marin J,Romaguera S.A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces[J].Fixed Point Theory,2014,40:1-8.
[12]Hadzic O,Pap E.Fixed point theory in probabilistic metric spaces.Mathematics and its Applicatins[M].Providence:Kliwer Academic Publishers,Dordrecht,2001.
[2]Hadzic O,Pap E.A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces[J].Fuzzy Sets Syst,2002,127:333-444.
[3]Hadzic O.Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces[J].Fuzzy Sets Syst,1989,29:115-125.
[4]Fang J X.A note on fixed point theorem of Hadzic[J].Fuzzy Sets Syst,1992,48:391-395.
[5]Xiao J Z,Zhu X H,Jin X.Fixed point theorem for nonlinear contractions in Kaleva-Seikkala’s type fuzzy metric spaces[J].Fuzzy Sets Syst,2012,200:65-83.
[6]Zhu J,Zhong C K,Wang G P.An extension of Ekeland’s variational principle in fuzzy metric spaces and its application[J].Fuzzy Sets Syst,1999,108:353-363.
[7]Jachymski J.Equivalent conditions and the Meir-Keeler type theorems[J].Math Anal Appl,1995,194:293-303.
[8]Boyd D W,Wong J S.On nonlinear contractions[J].Proc Am Math Soc,1969,20:458-464.
[9]Xiao J Z,Zhu X H.On linearly topological structure and property of fuzzy normed linear space[J].Fuzzy Sets Syst,2002,125:153-161.
[10]Xiao J Z,Zhu X H.Topological degree theory and fixed point theorems in fuzzy normed linear spaces[J].Fuzzy Sets Syst,2004,147:437-452.
[11]Alegre C,Marin J,Romaguera S.A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces[J].Fixed Point Theory,2014,40:1-8.
[12]Hadzic O,Pap E.Fixed point theory in probabilistic metric spaces.Mathematics and its Applicatins[M].Providence:Kliwer Academic Publishers,Dordrecht,2001.