منابع مشابه
Minimax Theorems on C1 Manifolds via Ekeland Variational Principle
Let X be a Banach space and Φ : X → R of class C1. We are interested in finding critical points for the restriction of Φ to the manifold M = {u ∈ X : G(u) = 1}, where G : X → R is a C1 function having 1 as a regular value. A point u ∈M is a critical point of the restriction of Φ to M if and only if dΦ(u)|TuM = 0 (see the definition in Section 2). Our purpose is to prove two general minimax prin...
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We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...
متن کاملA Remark on the Lower Semicontinuity Assumption in the Ekeland Variational Principle
What happens to the conclusion of the Ekeland variational principle (briefly, EVP) if a considered function f : X → R ∪ {+∞} is lower semicontinuous not on a whole metric space X but only on its domain? We provide a straightforward proof showing that it still holds but only for varying in some interval ]0, β − infX f [, where β is a quantity expressing quantitatively the violation of the lower ...
متن کامل$(varphi_1, varphi_2)$-variational principle
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Ma...
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By using a Danes̆’ drop theorem in locally convex spaces we obtain a vectorial form of Ekelandtype variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk’s fixed-point theorem, Takahashi’s nonconvex minimization theorem, and Oettli-Théra’s theorem. Furthermore, we show that these results are equivalent to each other. Also, the existen...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.08.004