一类具有集值映射的集值变分包含问题的解的存在性

Existence of Solutions for a Class of Set-valued Variational Inclusions

在没有光滑性的一般实Banach空间中构造了一类具有集值映射的变分包含问题,并利用预解算子技巧,给出了这类变分包含问题与一个不动点问题的等价性,然后借助于Banach压缩映射原理,在适当的条件下,证明了此类变分包含问题的解的存在唯一性.

We establish a class of variational inclusions with set-valued mappings in the general real Ba-nach space without smoothmers,then give this kind of variational inclusions and a fixed point problems of equivalence by using the resolvent operator technique,Finally,by using Banach contraction mapping theo-ry , under the right conditions,we proved that this kind of existence and uniqueness of the solution of vari-ational inclusions problem.