一类集值拟变分包含解的存在性定理

Existence Theory for A Kind of Generalized Nonlinear Set-valued Quasi-Variational Inclusionsand Resolvent Equations in Banach Spaces

研究一类新的集值拟变分包含,在实Hilbert空间中,利用预解算子技术,建立了集值拟变分包含、预解方程和不动点问题间的等价性。利用该等价性,建立了新的迭代算法,得到了这种变分包含解的存在性定理。该文提出的算法和结果推广和改进了近年来许多作者所作的算法和结果。

This paper studied a new set-valued quasi-variational inclusions. By using the properties of m-accretive, the equivalence between the generalized nonlinear set-valued quasi-variational inclusions, the resolvent equations, and the fixed-point problem in Banach spaces are established. Using the equivalence, some iterative algorithms for a new class of generalized nonlinear set-valued quasi-variational inclusions and related optimization problems is developed. The algorithms and results improve and generalize many known corresponding algorithms and results in resent years.