带ψ-强单调映象的广义非线性拟变分包含

摘要

In this paper, the author introduces and studies a new class of generalized nonlinear quasi-variational inclusions with ψ-strongly monotone mappings, and establish an existence theorem of solutions and constructs a new proximal point algorithm with errors for finding the approximate solutions for this class of generalized nonlinear quasi-variational inclusions by using the resolvent operator technique for maximal η-monotone mapping in Hilbert spaces. The convergence criteria for the algorithm is also discussed.%引入了一类新的带ψ-强单调映象的广义非线性拟变分包含.在Hilbert空间中使用极大η-单调映象的预解算子方法建立了这类变分包含解的存在性定理,构造了求此类变分包含解具误差的新迭代算法,并讨论了算法的收敛准则.