中山大学学报自然科学版 ›› 2015, Vol. 54 ›› Issue (5): 1-4.

• 研究论文 •    下一篇

具有Banach代数的锥度量空间上拟压缩映射的新不动点定理

许绍元1,马超2,周作领3   

  1. 1. 韩山师范学院数学与统计学系, 广东 潮州 521041;
    2. 澳门科技大学资讯科技学院,中国 澳门;
    3. 中山大学岭南学院, 广东 广州 510275
  • 收稿日期:2015-01-16 出版日期:2015-09-25 发布日期:2015-09-25
  • 通讯作者: 马超;E-mail:cma@must.edu.mo

A New Fixed Point Theorem of Quasi-Contractions on Cone Metric Space

XU Shaoyuan1, MA Chao2, ZHOU Zuoling3   

  1. 1. School of Mathematics and Statistics, Hanshan Normal College, Chaozhou 521041, China;
    2. Faculty of Information Technology, Macao University of Science and Technology, Macao, China;
    3. School of Lingnan, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2015-01-16 Online:2015-09-25 Published:2015-09-25

摘要:

以Banach代数取代Banach空间作为锥度量空间的底空间,引入具有Banach代数的锥度量空间,在正规性条件下已经得到了关于拟压缩映射的不动点定理。删去正规性条件,利用c-序列理论同样得到了拟压缩映射的不动点存在唯一性,主要结果改进和推广了相关文献的一些结论。

关键词: 具有Banach代数的锥度量空间, 非正规锥, 不动点定理, 拟压缩映射, c-序列

Abstract:

By replacing Banach spaces by Banach algebras as the underlying spaces of cone metric spaces, the concept of cone metric spaces with Banach algebras has been introduced. And a fixed point theorem of quasi-contractions with the assumption of normality has been proved. By omitting the assumption of normality and utilizing the theory of c-sequence, the existence and uniqueness of the fixed point for the quasi-contractions is obtained in the setting of cone metric spaces with Banach algebras. As a consequence, the corresponding result in the literature is improved and generalized.

Key words: cone metric spaces with Banach algebras, non-normal cones, fixed point theorems, quasi-contractions, c-sequence

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