中文摘要：

引入了一类新的广义非凸变分不等式，利用投影技巧建立该变分不等式与不动点问题的等价关系，进一步讨论逼近广义非凸变分不等式解的预测一校正投影算法，并在算子T具有g—γ-强单调性的条件下证明了相应迭代序列收敛到广义非凸变分不等式问题的解．

英文摘要：

A new class of extended general nonconvex variational inequalities is introduced. The equivalence between the extended general nonconvex variational inequality and the fixed point problem is established using essentially projection technique. This alternative equivalent formulation is used to suggest and analyze a predictor - corrector method for finding an approximate solution of the general nonconvex variational inequality. The con- vergence analysis of the corresponding iterative sequence are also considered under the condition of the underly- ing operator T with g - T - strongly monotone.