Ekeland Variational Principle, Minimax Theorems and Existence of Nonconvex Equilibria in Complete Metric Spaces

摘要

[[abstract]]In this paper, we introduce the concept of τ -function which generalizes the concept of w-distance studiedin the literature. We establish a generalized Ekeland’s variational principle in the setting of lower semicontinuousfrom above and τ -functions. As applications of our Ekeland’s variational principle, we derivegeneralized Caristi’s (common) fixed point theorems, a generalized Takahashi’s nonconvex minimizationtheorem, a nonconvex minimax theorem, a nonconvex equilibrium theorem and a generalized flower petaltheorem for lower semicontinuous from above functions or lower semicontinuous functions in the completemetric spaces. We also prove that these theorems also imply our Ekeland’s variational principle.© 2005 Elsevier Inc. All rights reserved.