一类广义非线性变分不等式解的存在性及迭代算法

Existence and iterative algorithm of solutions for a new class of generalized nonlinear variational inequalities

解决一类新的广义非线性变分不等式解问题,定义了强单调映射和Lipschitz连续性的概念,利用辅助原理和压缩映射原理,研究了包含强制连续双线性型a(u,v)和非线性型b(u,v)的变分不等式解的存在性,同时构造了一种新的迭代算法,证明了迭代算法的收敛性.文中的结果推广和改进了文献中的相应结论.

In order to solve a new class of generalized nonlinear variational inequalities prooblem, me aennlnon of strongly monotone mapping and Lipschitz continuous are given in this paper. Using the auxiliary principle technique, the existence theorem of solutions for this kind of generalized nonlinear variational inequalities, which involving a coercive continuous bilinear form a（u,v） and a nonlinear form b（u,v）, is investigated. Furthermore, the author has developed a new iterative scheme, and discussed the convergence of the sequence generated by the iterative algorithm. The results in this study have extended and improved the corresponding studies documented.