关于一类一般非线性变分不等式组

On a System of Generalized Nonlinear Variational Inqualities

设H是一个实的Hilbert空间,在H中引入了一类新的带有Lipschitz连续,强单调和松弛单调映射的一般非线性变分不等式组,利用投影的方法,建立了此类一般非线性变分不等式组与一个不动点问题的等价性是本文的主要工作,该结果推广了已知的一些结论。

Let H be a real Hilbert space,we introduce a new system of generalized nonlinear variational inqualities involving Lipschitz continuous,strongly monotone and relaxed monotone mappings in Hilbert space.Using projection method,we establish an equivalence between the system of generalized nonlinear variational inqualities and the fixed point problem,the results presented in this paper extend many known results.