关于一类广义非线性拟变分不等式

Study of Specific Version of Generalized Nonlinear Quasi-Variational Inequalities

引进了一种新的广义非线性拟变分不等式,使用预解算子技术建立了与其等价的不动点问题。利用这一等价关系,提出了两种迭代算法,并证明了带有极大单调映射的广义非线性拟变分不等式的解的存在性定理,证明了由算法产生的序列收敛性,其结果推广了某些已知结果。

A new version of general nonlinear quasi-variational inequalities was introduced.By using the technique of resolvent operator,the problem on the fixed points in equal value was established.With such equivalence,two different iterative algorithms were not only suggested,but also,the solution existence theorem on the general nonlinear quasi-variational inequalities with maximum monotone mappings was proved.The convergence for sequence generated by the algorithms was verified.The conclusions hereby have popularized a number of known conclusions.