Abstract
The new concepts of theZ-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in theZ-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 orderedZ-C-X space. Therefore, some new results are obtained.
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