Some Problems in the Z-C-X Space

• Published in: Applied mathematics and mechanics Vol. 23; no. 8; pp. 942 - 947
• Main Author: ZHU Chuan-xi(朱传喜)
• Format: Journal Article
• Language: English
• Published: Institute of Mathematics, Nanchang University, Nanchang 330029, P R China 01.08.2002; Research Center for Applied Mathematics and Institute of Information and System Science, Xi'an Jiaotong University, Xi'an 710049, P R China
• Subjects: 1-set; Banach; continuous; contractive; operator; random; real; semiclosed; separable; solution; space; Z-C-X; random continuous operator; random semiclosed 1-set contractive operator; separable real Banach space; Z-C-X space; random solution
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/BF02437799

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.