Applications of the KKM Property to Coincidence Theorems, Equilibrium Problems, Minimax Inequalities and Variational Relation Problems

作者：Patriche Monica

来源：Numerical Functional Analysis and Optimization, 2017, 38(4): 523-548.

DOI：10.1080/01630563.2017.1287085

• Coincidence theorem
• equilibrium problem
• KKM property
• minimax inequality
• variational relation problem
• 49J35
• 91B50

In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. To do this, we define new type of correspondences, namely, properly quasi-convex-like correspondences. Further, we apply the obtained theorems to solve equilibrium problems and to establish a minimax inequality. In the last part of the paper, we study the existence of solutions for generalized vector variational relation problems. Our analysis is based on the applications of the KKM principle. We establish existence theorems involving new hypothesis and we improve the results of some recent papers.

• 出版日期2017