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題名: Ekeland Variational Principle, Minimax Theorems and Existence of Nonconvex Equilibria in Complete Metric Spaces
作者: L. J. Lin;W. S. Du
貢獻者: 數學系
關鍵詞: τ -Function;Generalized Ekeland’s variational principle;Lower semicontinuous from above function;Generalized Caristi’s (common) fixed point theorem;Nonconvex minimax theorem;Nonconvex equilibrium
theorem;Generalized flower petal theorem
日期: 2006-11
上傳時間: 2011-05-10T06:48:50Z
出版者: Elsevier Science
摘要: 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.
關聯: Journal of Mathematical Analysis and Applications, 323(1):360-370
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