模糊度量空间中的循环广义(ф,ψ)-弱压缩映射
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摘要
为优化模糊度量空间中循环弱φ-压缩映射不动点结果,提出模糊度量空间中的循环广义(ф,ψ)-弱压缩映射的概念。运用构造迭代序列方法证明了该映射在G-完备模糊度量空间中的不动点定理,并用例子说明了该结果的实用性,结果推广了Gopal等得到的模糊度量空间中循环弱φ-压缩映射的不动点定理。
In order to optimize the fixed point results of cyclicφ-weakly contractive mapping in fuzzy metric spaces,it presents the concept of cyclic generalized (ф,ψ)-weakly contractive mappings in fuzzy metric spaces.It proves the fixed point theory of the cyclic generalized (ф,ψ)-weakly contractive mappings in Gcomplete fuzzy metric spaces by using the method of constructing iterative sequence.And an example is given to illustrate the usefulness of the results.The result generalizes the fixed point theorem of cyclicφ-weakly contractive mapping in fuzzy metric spaces obtained by Gopal et al.
In order to optimize the fixed point results of cyclicφ-weakly contractive mapping in fuzzy metric spaces,it presents the concept of cyclic generalized (ф,ψ)-weakly contractive mappings in fuzzy metric spaces.It proves the fixed point theory of the cyclic generalized (ф,ψ)-weakly contractive mappings in Gcomplete fuzzy metric spaces by using the method of constructing iterative sequence.And an example is given to illustrate the usefulness of the results.The result generalizes the fixed point theorem of cyclicφ-weakly contractive mapping in fuzzy metric spaces obtained by Gopal et al.
引文
[1]Zadeh L A.Fuzzy Sets[J].Inform and Control,1965,8(3):338-353.
[2]Kramosil O,Michálek J.Fuzzy metrics and statistical metric spaces[J].Kybernetika,1975,11(5):336-344.
[3]George A,Veeramani P.On some results in fuzzy metric spaces[J].Fuzzy Sets and Systems,1994,64(3):395-399.
[4]Khan M S,Swaleh M,Sessa S.Fixed point theorems by altering distances between the points[J].Bulletin of the Australian Mathematical Society,1984,30(1):1-9.
[5]Rhoades B E.Some theorems on weakly contractive maps[J].Nonlinear Analysis Theory Methods and Applications,2001,47(4):2683-2693.
[6]Vetro C,Gopal D,Imdad M.Common fixed point theorems forφ,(ψ)-weak contractions in fuzzy metric spaces[J].Indian Journal of Mathematics,2010,52(3):1-18.
[7]Kirk W A,Srinivasan P S,Veeramani P.Fixed points for mapping satisfying cyclic contractive conditions[J].International Journal on Fixed Point Theory Computation and Applications,2003,1(1):79-89.
[8]Gopal D,Imdad M,Vetro C et al.Fixed point theory for cyclic weakφ-contraction in fuzzy metric spaces[J].Journal of Nonlinear Analysis and Application,2012,2012:1-11.
[9]Shukla S,Chauhan S.Fuzzy cyclic contraction and fixed point theorems[J].Journal of the Egyption Mathematical Society,2015,23(1):139-143.
[10]Prapoorna M,Rangamma M.Fixed points ofψ,(φ)-almost weakly contractive maps in fuzzy metrics paces[J].Fixed Point Theory,2016,6(4):387-396.
[11]Sangurlu M,Turkoglu D.Fixed point theorems forψ(φ)-contractions in a fuzzy metric spaces[J].Journal of Nonlinear Science and Applications,2015,8(5):687-694.
[12]Schweizer B,Sklar A.Statistical metric spaces[J].Pacific Journal of Mathematics,1960,10(10):313-334.
[13]Pacurar M,Rus I A.Fixed point theory for cyclicφ-contractions[J].Nonlinear Analysis,2010,72(3):1181-1187.
[14]Grabiec M.Fixed points in fuzzy metric spaces[J].Fuzzy Sets and Systems,1988,27(3):385-389.
[15]Rodríguez-López J,Romaguera S.The Hausdorff fuzzy metric on compact sets[J].Fuzzy Sets and Systems,2004,147(2):273-283.
[2]Kramosil O,Michálek J.Fuzzy metrics and statistical metric spaces[J].Kybernetika,1975,11(5):336-344.
[3]George A,Veeramani P.On some results in fuzzy metric spaces[J].Fuzzy Sets and Systems,1994,64(3):395-399.
[4]Khan M S,Swaleh M,Sessa S.Fixed point theorems by altering distances between the points[J].Bulletin of the Australian Mathematical Society,1984,30(1):1-9.
[5]Rhoades B E.Some theorems on weakly contractive maps[J].Nonlinear Analysis Theory Methods and Applications,2001,47(4):2683-2693.
[6]Vetro C,Gopal D,Imdad M.Common fixed point theorems forφ,(ψ)-weak contractions in fuzzy metric spaces[J].Indian Journal of Mathematics,2010,52(3):1-18.
[7]Kirk W A,Srinivasan P S,Veeramani P.Fixed points for mapping satisfying cyclic contractive conditions[J].International Journal on Fixed Point Theory Computation and Applications,2003,1(1):79-89.
[8]Gopal D,Imdad M,Vetro C et al.Fixed point theory for cyclic weakφ-contraction in fuzzy metric spaces[J].Journal of Nonlinear Analysis and Application,2012,2012:1-11.
[9]Shukla S,Chauhan S.Fuzzy cyclic contraction and fixed point theorems[J].Journal of the Egyption Mathematical Society,2015,23(1):139-143.
[10]Prapoorna M,Rangamma M.Fixed points ofψ,(φ)-almost weakly contractive maps in fuzzy metrics paces[J].Fixed Point Theory,2016,6(4):387-396.
[11]Sangurlu M,Turkoglu D.Fixed point theorems forψ(φ)-contractions in a fuzzy metric spaces[J].Journal of Nonlinear Science and Applications,2015,8(5):687-694.
[12]Schweizer B,Sklar A.Statistical metric spaces[J].Pacific Journal of Mathematics,1960,10(10):313-334.
[13]Pacurar M,Rus I A.Fixed point theory for cyclicφ-contractions[J].Nonlinear Analysis,2010,72(3):1181-1187.
[14]Grabiec M.Fixed points in fuzzy metric spaces[J].Fuzzy Sets and Systems,1988,27(3):385-389.
[15]Rodríguez-López J,Romaguera S.The Hausdorff fuzzy metric on compact sets[J].Fuzzy Sets and Systems,2004,147(2):273-283.