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Title: Ekeland Variational Principle, Minimax Theorems and Existence of Nonconvex Equilibria in Complete Metric Spaces
Authors: L. J. Lin;W. S. Du
Contributors: 數學系
Keywords: τ -Function;Generalized Ekeland’s variational principle;Lower semicontinuous from above function;Generalized Caristi’s (common) fixed point theorem;Nonconvex minimax theorem;Nonconvex equilibrium
;Generalized flower petal theorem
Date: 2006-11
Issue Date: 2011-05-10T06:48:50Z
Publisher: Elsevier Science
Abstract: In this paper, we introduce the concept of τ -function which generalizes the concept of w-distance studied
in the literature. We establish a generalized Ekeland’s variational principle in the setting of lower semicontinuous
from above and τ -functions. As applications of our Ekeland’s variational principle, we derive
generalized Caristi’s (common) fixed point theorems, a generalized Takahashi’s nonconvex minimization
theorem, a nonconvex minimax theorem, a nonconvex equilibrium theorem and a generalized flower petal
theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete
metric spaces. We also prove that these theorems also imply our Ekeland’s variational principle.
© 2005 Elsevier Inc. All rights reserved.
Relation: Journal of Mathematical Analysis and Applications, 323(1):360-370
Appears in Collections:[數學系] 期刊論文

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