广义强非线性拟变分不等式

GENERALIZED STRONGLY NONLINEAR QUASI VARIATIONAL INEQUALITIES

引入并研究一类新的广义强非线性拟变分不等式，构造新的迭代算法，在没有紧性条件下，证明这类拟变分不等式解的存在性及由算法生成的迭代序列的收敛性．

A new class of generalized strongly nonlinear quasi variational inequalities for set valued mappings are introduced and studied. Let H be a Hilbert space, D a nonempty subset of H, K a nonempty closed convex subset of H . Let N:H×H→H be a nonlinear mappings, f,g:H→H and S、T、K:D→CB(H) set valued mappings. For the following problem:Find x∈D, u∈S(x),v∈T(x) such tha t g(x)∈D(x) and 〈f(x)-N(u,v),y-g(x)〉≥0,y∈K(x). The author constructed a new iterative algorithm for this class of generalized strongly nonlinear quasi variational inequalities, proved the existence of solutions for this class of generalized strongly nonlinear quasi variational inequalities for set valued mappings without compactness and the convergence of sequences generated by the algorithm. Those results extend and improve the earlier and recent works of several authors.