In this paper we introduce extended generalized complementarity problems in Hausdorff topological vector spaces in duality and study the existence of their solutions. We use a different method than those in literature on the existence of solutions of complementarity problems, which are usually based on arguments from generalized monotonicity. This leads us to obtain new results and improve many existing results in literature. We also prove some existence results for extended generalized complementarity problems in reflexive Banach spaces by means of a Tikhonov regularization procedure under a copositivity assumption and arguments from the recession analysis.

在本文中，我们介绍了双重对偶的Hausdorff拓扑向量空间中的扩展广义互补问题，并研究了其解的存在性。关于互补性问题的解的存在，我们使用与文献中不同的方法，通常基于广义单调性的论点。这使我们获得了新的结​​果，并改善了文献中的许多现有结果。我们还通过Tikhonov正则化程序在共性假设和衰退分析的论证下，证明了自反Banach空间中扩展的广义互补问题的一些存在结果。