例外簇元与集值互补问题

摘要

在文献［5-10］中Isac等人发现当多值互补问题无解时，与之相联系的映象一定存在一个序列满足一组条件，Isac等人称这个序列为例外簇，另一方面，当多值互补问题有解时，与之相联系的映象一定不存在例外簇。该文证明了几类互补理论所涉及的非线性映象没有例外簇元，并得出与之相联系的集值互补问题（MCP）是可解的。%Some mathematicians, such as lsac, found out that, in literature 5 - 10, there exists a certain group of conditions for certain mappings relating to no solution to multi - valued complementary problems, it is called exceptional family; and also, if there are solutions, there is no this kind of family. This paper is to prove that the corresponding complementary problems are solvable by identifying some classes of nonlinear tunctions without exceptional families of elements