Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2018, Vol. 54 ›› Issue (4): 693-698.DOI: 10.13209/j.0479-8023.2017.184

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Fixed Point Theorems under c-Distance in Cone Metric Spaces over Banach Algebras

HUANG Huaping, DENG Guantie   

  1. Laboratory of Mathematics and Complex Systems (MOE), School of Mathematical Sciences, Beijing Normal University, Beijing 100875
  • Received:2017-04-05 Revised:2017-09-12 Online:2018-07-20 Published:2018-07-20
  • Contact: DENG Guantie, E-mail: denggt(at)


黄华平, 邓冠铁   

  1. 北京师范大学数学科学学院, 数学与复杂系统教育部重点实验室, 北京 100875
  • 通讯作者: 邓冠铁, E-mail: denggt(at)
  • 基金资助:


The authors obtain several theorems of the existence and uniqueness of fixed point for contractive mappings under c-distance in cone metric spaces over Banach algebras without the assumptions of normality of cones and the continuity of mappings. The results greatly improve and complement some previous results. Moreover, a supportive example to illustrate the main assertions is also given. Otherwise, by solving the problem of existence and uniqueness for an elementary equation, a significant application for the obtained results is presented.

Key words: cone metric space over Banach algebra, c-distance, continuity, normality, fixed point


在不考虑映射的连续性和锥的正规性条件下, 得到赋值Banach代数的锥度量空间中c-距离意义下压缩型映射不动点的存在性和唯一性定理, 在很大程度上改进和补充了前人的结果, 并举例验证了得到的结论。另外, 通过解决一个初等方程解的存在性和唯一性问题, 说明了所得结果的一个重要应用。

关键词: 赋值Banach代数的锥度量空间; c-距离, 连续性, 正规性, 不动点

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