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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (8): 942-947.

• 论文 • 上一篇    下一篇

SOME PROBLEMS IN THE Z-C-X SPACE

朱传喜   

  1. 1. Research Center for Applied Mathematics and Institute of Information and System Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China;
    2. Institute of Mathematics, Nanchang University, Nanchang 330029, P. R. China
  • 收稿日期:2001-03-30 修回日期:2002-04-23 出版日期:2002-08-18 发布日期:2002-08-18
  • 基金资助:
    the Natural Science Foundation of Jiangxi Province(0011022)

SOME PROBLEMS IN THE Z-C-X SPACE

ZHU Chuan-xi   

  1. 1. Research Center for Applied Mathematics and Institute of Information and System Science, Xi’an Jiaotong University, Xi’an 710049, P. R. China;
    2. Institute of Mathematics, Nanchang University, Nanchang 330029, P. R. China
  • Received:2001-03-30 Revised:2002-04-23 Online:2002-08-18 Published:2002-08-18
  • Supported by:
    the Natural Science Foundation of Jiangxi Province(0011022)

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摘要： The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman’s theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.

Abstract: The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman’s theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.

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