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复值度量空间上满足分式收缩条件的映射族的唯一公共不动点

Unique Common Fixed Points for Mappings Satisfying Rational Contractions on Complex Valued Metric Spaces
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摘要 指出了文献[Int.J.Pure Appl.Math.,2011,73(2):159-164]中给出的定理的错误证明,得出复值度量空间上满足分式收缩条件的四个映射的唯一公共不动点定理,并给出了若干更一般形式的结论及不动点定理.所得结论推广和改进了一些已知结果. We point out a false proof of a given theorem in [Int. J. Pure Appl. Math.,2011, 73（2）： 159-164], and obtain unique common fixed theorems for four mappings satisfying a rational contractive condition on complex valued metric spaces and give some more general results and fixed point theorems. The obtained results generalize and improve some known conclusions.
作者 朴勇杰
机构地区 延边大学理学院数学系
出处 《数学进展》 CSCD 北大核心 2016年第4期581-588,共8页 Advances in Mathematics（China）
基金 国家自然科学基金(No.11361064)
关键词 复值度量空间 分式收缩条件 Cauchy序列 公共不动点 complex valued metric space rational contractive condition Cauchy sequence common fixed point
分类号 O189.11 [理学—基础数学] O177.91 [理学—基础数学]
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参考文献12

  • 1Azam, A., Fisher, B. and Khan, M., Common fixed point theorems in complex valued metric spaces, N.amer. Funct. Anal. Optim., 2011, 32(3): 243-353.
  • 2Bari, C.D. and Vetro, P.,-pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 2008, 57(2): 279-285.
  • 3Beg, I., Azam, A. and Arshad, M., Common fixed points for maps on topological vector space valued cone metric spaces, Int. J. Math. Math. Sci., 2009, 2009: Article ID 560264, 8 pages.
  • 4Bhatt, S., Chaukiyal, S. and Dimri, R.C., Common fixed point of mappings satisfying rational inequality in complex valued metric spaces, Int. J. Pure Appl. Math., 2011, 73(2): 159-164.
  • 5Bhatt, S., Chaukiyal, S. and Dimri, R.C., A common fixed point theorem for weakly compatible maps in complex valued metric spaces, Int. J. Math. Sci. Appl., 2011, 1(3): 1385-1389.
  • 6Huang, L.G. and Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, Y. Math. Anal. Appl., 2007, 332(2): 1468-1476.
  • 7Nashine, H.K, Imbad, M. and Hasan, M., Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl., 2014, 7: 42-50.
  • 8Piao, Y.J., Common fixed points for two mappings with expansive properties in complex valued metric spaces, J. Chungcheong Math. Soc., 2015, 28(1): 11-28.
  • 9Rouzkard, F. and Imdad, M., Some common fixed point theorems on complex valued metric spaces, C'omput. Math. Appl., 2012, 64(6): 1866-1874.
  • 10Sintunavarat, W. and Kumam, P., Generalized common fixed point theorems in complex valued metric spaces and application, J. Inequal. Appl., 2012, 2012: Article ID 84, 12 pages.
数学进展
2016年 第4期

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