模糊度量空间中模糊广义H-弱压缩映射
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摘要
提出模糊度量空间中模糊广义H-弱压缩映射的概念,并运用构造迭代序列方法证明了在模糊度量M一致连续的条件下,模糊广义H-弱压缩映射在M-完备的模糊度量空间中存在唯一的不动点.该结论从本质上推广了模糊H-弱压缩映射的概念及其不动点定理.
In this paper,the concept of fuzzy generalized H-weak contractive mapping is proposed in fuzzy metric space.It is proved that fuzzy generalized H-weak contractive mapping has the unique fixed point in M-complete fuzzy metric spaces by constructing iterative sequence,which is founded under the condition of uniformly continuity of the M-fuzzy measure.The concept and fixed theory of fuzzy H-weak contractive mapping are really generalized.
In this paper,the concept of fuzzy generalized H-weak contractive mapping is proposed in fuzzy metric space.It is proved that fuzzy generalized H-weak contractive mapping has the unique fixed point in M-complete fuzzy metric spaces by constructing iterative sequence,which is founded under the condition of uniformly continuity of the M-fuzzy measure.The concept and fixed theory of fuzzy H-weak contractive mapping are really generalized.
引文
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[3]WARDOWSKI D.Fuzzy contractive mappings and fixed points in fuzzy metric spaces[J].Fuzzy Sets&Syst,2013,222(5):108-114.
[4]SHUKLA S.Fuzzy H-weak contractions and fixed point theorems in fuzzy metric spaces[J].Gulf J Math,2013,1(2):171-179.
[5]AMINI-HARANDI A.Fixed points of fuzzy generalized contractive mappings in fuzzy metric spaces[J].Iran J Fuzzy Syst,2014,11(2):113-120.
[6]SHUKLA S,CHAUHAN S.Fuzzy cyclic contraction and fixed point theorems[J].J Egypt Math Soc,2015,23(1):139-143.
[7]PRAPOORNA M,RANGAMMA M.Fixed points of(ψ,Φ)-almost weakly contractive maps in fuzzy metric spaces[J].Adv Fixed Point Theory,2016,6(4):387-396.
[8]ROLDAN-LOPEZ-de-HIERRO A F,SINTUNAVARAT W.Common fixed point theorems in fuzzy metric spaces using the CLRg property[J].Fuzzy Sets&Syst,2016,282(1):131-142.
[9]GREGORI V,MINANA J J.On fuzzyψ-contractive sequences and fixed point theorems[J].Fuzzy Sets&Syst,2016,300(1):93-101.
[10]WANG Shuang.Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property[J].J Nonlinear Sci Appl,2016,9(1):1043-1051.
[11]ALEGRE C,ROMAGUERA S.A note onφ-contractions in probabilistic and fuzzy metric spaces[J].Fuzzy Sets&Syst,2017,313(1):119-121.
[12]SINTUNAVARAT W,KUMAM P.Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces[J].J Appl Math,2011,2011(2):1-14.
[2]GREGORI V,SAPENA A.On fixed-point theorems in fuzzy metric spaces[J].Fuzzy Sets&Syst,2002,125(2):245-252.
[3]WARDOWSKI D.Fuzzy contractive mappings and fixed points in fuzzy metric spaces[J].Fuzzy Sets&Syst,2013,222(5):108-114.
[4]SHUKLA S.Fuzzy H-weak contractions and fixed point theorems in fuzzy metric spaces[J].Gulf J Math,2013,1(2):171-179.
[5]AMINI-HARANDI A.Fixed points of fuzzy generalized contractive mappings in fuzzy metric spaces[J].Iran J Fuzzy Syst,2014,11(2):113-120.
[6]SHUKLA S,CHAUHAN S.Fuzzy cyclic contraction and fixed point theorems[J].J Egypt Math Soc,2015,23(1):139-143.
[7]PRAPOORNA M,RANGAMMA M.Fixed points of(ψ,Φ)-almost weakly contractive maps in fuzzy metric spaces[J].Adv Fixed Point Theory,2016,6(4):387-396.
[8]ROLDAN-LOPEZ-de-HIERRO A F,SINTUNAVARAT W.Common fixed point theorems in fuzzy metric spaces using the CLRg property[J].Fuzzy Sets&Syst,2016,282(1):131-142.
[9]GREGORI V,MINANA J J.On fuzzyψ-contractive sequences and fixed point theorems[J].Fuzzy Sets&Syst,2016,300(1):93-101.
[10]WANG Shuang.Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the CLRg property[J].J Nonlinear Sci Appl,2016,9(1):1043-1051.
[11]ALEGRE C,ROMAGUERA S.A note onφ-contractions in probabilistic and fuzzy metric spaces[J].Fuzzy Sets&Syst,2017,313(1):119-121.
[12]SINTUNAVARAT W,KUMAM P.Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces[J].J Appl Math,2011,2011(2):1-14.