Banach空间中一类变分包含解的存在性和唯一性

为了解决Banach空间中一类变分不等式的包含解问题,给出了正规对偶映射、k强增生映射、次微分的概念,利用强增生映射性质证明了复合型映射的强增生性,并证明了对偶空间中,变分包含问题的不动点的存在性.利用一般的对偶原理和不动点理论,证明了自反Banach空间中,满足G teaux微分和k-强增生映射的某一类变分不等式包含解的存在性和唯一性.该结果将许多相关文献中的变分包含问题由"光滑的Banach空间"推广到"自反的Banach空间",扩大了变分不等式包含解问题应用范围.

Existence and uniqueness of solutions for a class of variational inclusion problem in Banach spaces

In order to solve a class of variational inclusion problem in Banach spaces,the definition of normalized duality mapping,k-strongly accretive mapping,and order differential are given in this paper.Using the properties of k-strongly accretive,the authors prove that the compound mapping is strongly accretive,and also prove the existence of fixed point of variational inclusion problem in dual space.In addition,the authors use general duality principle and fixed point theory to prove that the existence and uniqueness of solutions for the class of variational inclusion problem,which satisfies Gteaux differential and k-Strongly accretive mapping.This study result generalizes variational inclusion problem from "smooth Banach spaces" into "reflexive Banach spaces",and extends the application range of variational inclusion problem.