对广义强非线性拟变分包含带有误差的近似点算法

Proximal Point Algorithm with Errors for Generalized Strongly Nonlinear Quasivariational Inclusions

本文研究了一类广义强非线性拟变分包含·在Ｈｉｌｂｅｒｔ空间内利用与极大单调映象相联系的预解算子的性质，对广义强非线性拟变分包含建立了解的存在性定理和建议了一个新的寻求近似解的带有误差的近似总算法，证明了近似解序列强收敛于精确解·作为特例，在此领域内的某些已知结果也被讨论·

n this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion and is established a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.