Banach空间中的广义集值变分包含和预解算子

Generalized Set-Valued Variational Inclusions and Resolvent Equations in Banach Spaces

研究了Banach空间的广义集值变分包含。首先指出了J U Jeong所著文章《Generalized set-valuedvariational inclusions and resolvent equations in Banach spaces》中的定理3.1是不成立的,然后借助预解算子技巧,建立了与广义变分包含相关的迭代算法,并给出了广义变分包含的迭代收敛定理,从而更正了该定理。

A class of generalized set - valued variational inclusions is studied. Firstly, we point out that the theorem 3.1 in J. U. Jeong＇s article ＂ Generalized set - valued variational inclusions and resolvent equations in Banach spaces＂ is untenable. Secondly, by using the resolvent operator technique, we establish the iterative algo- rithm and give the approximate solution for the generalized set -valued variational inclusions in Banach space. The result corrects the theorem.