拓扑矢量空间中的随机混合似变分不等式(英)

本文在Ｈａｕｓｄｏｒｆ拓扑矢量空间和Ｂａｎａｃｈ空间内研究了一类随机混合似变分不等式．由应用Ｔａｒａｆｄａｒ和Ｙｕａｎ的随机极小极大不等式，随机混合似变分不等式随机解的几个存在唯一性定理被证明．由使用辅助问题技巧，对在Ｂａｎａｃｈ空间内计算随机混合似变分不等式的近似解，作者建议和分析了一个十分一般的算法．最后收敛性准则也被讨论．这些定理和算法推广了许多已知结果．

RANDOM MIXED VARIATIONAL LIKE INEQUALITIES IN TOPOLOGICAL VECTOR SPACE

In this paper, author studies a class of random mixed variational like inequalities in Hausdorff topological vector spaces and Banach spaces. By applying a random minimax inequality due to Tarafdar and Yuan, several existence uniqueness theorems of random solutions for the random mixed variational like inequalities are proved. Next, by using auxiliary problem technique, author suggests and analyzs a quite general algortithm to compute the approximate random solutions for the random mixed variational like inequalities in Banach space. Finally, the convergence criteria is also dicussed. These theorems, algorithm and convergence results generalize the corresponding results of Parida Sahoo Kumar, Dien, Ding, Noor, Yao, Cohen and others to random version under Hausdorff topological space setting and Banach space setting.