含H-单调映象的广义非线性集值变分包含

Generalized Nonlinear Set-valued Variational Inclusions Involving H-monotone Mappings

引入和研究了一类新的含H-单调映象的广义非线性集值变分包含,在H ilbert空间中使用与H-单调映象相联系的预解算子性质,对这类广义非线性集值变分包含建立了解的存在性定理和构造了一种新的迭代算法,证明了由此算法生成的迭代序列强收敛于精确解.其算法和结果是最近文献中相应算法和结果的改进和推广.

A new class of generalized nonlinear set-valued variational inclusions involving H-monotone mapping are introduced and studied. By using the properties of the resolvent operator associated with a H-monotone mappings in Hilbert spaces. An existence theorem of solution for the generalized nonlinear set-valued variational inclusions involving H-monotone mappings is established and a new algorithn is constructed. The author proves the iterative sequences generated by the algorithm strongly converge to its exact solution. Our results improve and generalized known corresponding and results.