锥度量空间中c-距离下非连续映射的公共不动点定理
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摘要
在不要求映射的连续性,也不要求锥的正规性的条件下,获得了锥度量空间中,c-距离下两个映射的公共不动点定理.定理的结论上不仅得到了公共不动点的存在性,还得到其唯一性,改进和推广了原有的许多重要结果,同时给出了相应的例子.
In this paper, some new common fixed point results for two contractive mappings under c-distance in cone metric spaces are obtained, without appealing to continuous for mapping or normality for cone in the conditions. Furthermore, not only the existence but also the uniqueness of the common fixed point is gained. The results improve and generalize some well-known comparable results. Some supporting examples are given.
In this paper, some new common fixed point results for two contractive mappings under c-distance in cone metric spaces are obtained, without appealing to continuous for mapping or normality for cone in the conditions. Furthermore, not only the existence but also the uniqueness of the common fixed point is gained. The results improve and generalize some well-known comparable results. Some supporting examples are given.
引文
[1]Huang Longguang,Zhang Xian.Cone metric space and fixed point theorems of contractive mappings[J].J Math Anal Appl,2007,332:1468-1476.
[2]Mujahid A,Jungck G,Common fixed point results for noncommuting mappings without continuity in cone metric spaces[J].J Math Anal Appl.2008,341:416-420.
[3]Mujahid A,Rhoades B E.Fixed and periodic point results in cone metic spaces[J].Appl Math Letter,2009,22:511-515.
[4]Nashie H K,Rohen Y,Thokchom C.Common coupled fixed point theorems of two mappings satisfying generalized contractive condition in cone metric space[J].Internat J Pure Appl Math,2016,106(3):791-799.
[5]Kadelburg Z,Pavlovic M,Radenovic S,Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces[J].Comput Math Appl,2010,59:3148-3159.
[6]Cho Yeol Je,Reza Saadati,Wang Shenghua.Common fixed point theorems on generalized distance in ordered cone metric spaces[J].Comput Math Appl,2011,61:1254-1260.
[7]Kada O,Suzuki Tomonari and Takahashi Wataru.Nonconvex minimization theorems and fixed point theorems in complete metric spaces[J].Math Japonica,1996,44:381-391.
[8]Zaid Mohammed Fadail,Abd Ghafur Bin Ahmad,Ljiljana Paunovic.New fixed point results of single-valued mapping for c-distance in cone metric spaces[J].Fix Point Theory Appl,2012,doi:10.1155/2012/639713.
[9]Sintunavarat Wutiphol,Cho Yeol Je,Kumam Poom.Common fixed point theorems for c-distance in ordered cone metric spaces[J].Comput Math Appl,2011,62:1969-1978.
[10]Dorevi M,Dori C D,Kadelburg Z,Radenovic S,Spasic D.Fixed point results under c-distance in tvs-cone metric spaces[J].Fix Point Theory Appl,2011,doi:10.1186/1687-1812-2011-29.
[11]Hassen A,Erdal K,Sirous M.Coincidence points for expansive mappings under c-distance in cone metric space[J].Internat J Math Math Sci,2012,2012-6-6,doi:10.1155/2012/308921.
[12]Huang Huaping,Radenovi′c S,Doˇsenovi′c T.Some common fixed point theorems on c-distance in cone metric spaces over Banach algebras[J].Comput Math,2015,14(2):180-193.
[13]韩艳,张建元.锥度量空间中c-距离下的不动点定理[J].纯粹数学与应用数学,2015,31(6):581-587.
[14]Fadail Z M,Ahmad A G B,Golubovi′c Z.Fixed point theorems of single-valued mapping for c-distance in cone metric spaces[J].Abstr Appl Anal,2012,Article ID 826815,11 pages.
[15]Rahimi H,Rad G S,Kumam P.Generalized distance and new fixed point results[J].AsianEuropean J Math,2015,doi:10.1142/S1793557116500443.
[16]Yang Young-Oh,Choi Hong Joon.Fixed point theorems in ordered cone metric spaces[J].J Nonlinear Sci Appl,2016,9:4571-4579.
[17]Rahimi H,Rad G S.Common fixed-point theorems and c-distance in ordered cone metric spaces[J].Ukrain Math J,2014,65(12):1845-1861.
[18]张石生.不动点理论及应用[M].重庆:重庆出版社,1984.
[19]张宪,锥度量空间中Lipschitz型映射的公共不动点定理[J].数学学报,2010,53(6):1139-1148.
[2]Mujahid A,Jungck G,Common fixed point results for noncommuting mappings without continuity in cone metric spaces[J].J Math Anal Appl.2008,341:416-420.
[3]Mujahid A,Rhoades B E.Fixed and periodic point results in cone metic spaces[J].Appl Math Letter,2009,22:511-515.
[4]Nashie H K,Rohen Y,Thokchom C.Common coupled fixed point theorems of two mappings satisfying generalized contractive condition in cone metric space[J].Internat J Pure Appl Math,2016,106(3):791-799.
[5]Kadelburg Z,Pavlovic M,Radenovic S,Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces[J].Comput Math Appl,2010,59:3148-3159.
[6]Cho Yeol Je,Reza Saadati,Wang Shenghua.Common fixed point theorems on generalized distance in ordered cone metric spaces[J].Comput Math Appl,2011,61:1254-1260.
[7]Kada O,Suzuki Tomonari and Takahashi Wataru.Nonconvex minimization theorems and fixed point theorems in complete metric spaces[J].Math Japonica,1996,44:381-391.
[8]Zaid Mohammed Fadail,Abd Ghafur Bin Ahmad,Ljiljana Paunovic.New fixed point results of single-valued mapping for c-distance in cone metric spaces[J].Fix Point Theory Appl,2012,doi:10.1155/2012/639713.
[9]Sintunavarat Wutiphol,Cho Yeol Je,Kumam Poom.Common fixed point theorems for c-distance in ordered cone metric spaces[J].Comput Math Appl,2011,62:1969-1978.
[10]Dorevi M,Dori C D,Kadelburg Z,Radenovic S,Spasic D.Fixed point results under c-distance in tvs-cone metric spaces[J].Fix Point Theory Appl,2011,doi:10.1186/1687-1812-2011-29.
[11]Hassen A,Erdal K,Sirous M.Coincidence points for expansive mappings under c-distance in cone metric space[J].Internat J Math Math Sci,2012,2012-6-6,doi:10.1155/2012/308921.
[12]Huang Huaping,Radenovi′c S,Doˇsenovi′c T.Some common fixed point theorems on c-distance in cone metric spaces over Banach algebras[J].Comput Math,2015,14(2):180-193.
[13]韩艳,张建元.锥度量空间中c-距离下的不动点定理[J].纯粹数学与应用数学,2015,31(6):581-587.
[14]Fadail Z M,Ahmad A G B,Golubovi′c Z.Fixed point theorems of single-valued mapping for c-distance in cone metric spaces[J].Abstr Appl Anal,2012,Article ID 826815,11 pages.
[15]Rahimi H,Rad G S,Kumam P.Generalized distance and new fixed point results[J].AsianEuropean J Math,2015,doi:10.1142/S1793557116500443.
[16]Yang Young-Oh,Choi Hong Joon.Fixed point theorems in ordered cone metric spaces[J].J Nonlinear Sci Appl,2016,9:4571-4579.
[17]Rahimi H,Rad G S.Common fixed-point theorems and c-distance in ordered cone metric spaces[J].Ukrain Math J,2014,65(12):1845-1861.
[18]张石生.不动点理论及应用[M].重庆:重庆出版社,1984.
[19]张宪,锥度量空间中Lipschitz型映射的公共不动点定理[J].数学学报,2010,53(6):1139-1148.