Set-Valued Analysis

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Existence of intransitive equilibria in nonconvex economies
Set-Valued Analysis - Tập 3 - Trang 307-337 - 1995
Pascal Gourdel
We consider a general equilibrium model of an economy with increasing returns to scale or more general types of nonconvexity and without ordered preferences. Firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other firms. We suppose, moreover, that the pricing rule of the firms verifies a condition of weak bounded losses. This in...... hiện toàn bộ
Comparative Properties of Three Metrics in the Space of Compact Convex Sets
Set-Valued Analysis - Tập 5 - Trang 267-289 - 1997
Phil Diamond, Peter Kloeden, Alexander Rubinov, Alexander Vladimirov
Along with the Hausdorff metric, we consider two other metrics on the space of convex sets, namely, the metric induced by the Demyanov difference of convex sets and the Bartels–Pallaschke metric. We describe the hierarchy of these three metrics and of the corresponding norms in the space of differences of sublinear functions. The completeness of corresponding metric spaces is demonstrated. Conditi...... hiện toàn bộ
Lower Semicontinuity of the Solution Map to a Parametric Generalized Variational Inequality in Reflexive Banach Spaces
Set-Valued Analysis - Tập 16 - Trang 1089-1105 - 2008
B. T. Kien
This paper is concerned with the study of solution stability of a parametric generalized variational inequality in reflexive Banach spaces. Under the requirements that the operator of a unperturbed problem is of class (S) +  and operators under consideration are pseudo-monotone and demicontinuous, we show that the solution map of a parametric generalized variational inequality is lower semicontinu...... hiện toàn bộ
Hyperspaces of Banach Spaces with the Attouch—Wets Topology
Set-Valued Analysis - Tập 12 - Trang 329-344 - 2004
Katsuro Sakai, Masato Yaguchi
Let X be an infinite-dimensional Banach space with weight τ. By Cld AW (X), we denote the hyperspace of nonempty closed sets in X with the Attouch—Wets topology. By Fin AW (X), Comp AW (X) and Bdd AW (X), we denote the subspaces of Cld AW ...... hiện toàn bộ
On the Inexistence of Additive Equi-Lipschitzian Parametrizations of Compact Convex Subsets
Set-Valued Analysis - Tập 14 - Trang 319-326 - 2006
Pedro Terán
A Banach space of dimension at least 2 does not admit an equi-Lipschitzian family of additive mappings parametrizing all non-empty compact convex sets. Examples of linear Lipschitzian as well as positively homogeneous equi-Lipschitzian parametrizations exist in the literature.
Eigenvalue Problems for Hemivariational Inequalities
Set-Valued Analysis - Tập 16 - Trang 1061-1087 - 2008
Nikolaos S. Papageorgiou, Sandrina Rafaela Andrade Santos, Vasile Staicu
We consider a semilinear eigenvalue problem with a nonsmooth potential (hemivariational inequality). Using a nonsmooth analog of the local Ambrosetti–Rabinowitz condition (AR-condition), we show that the problem has a nontrivial smooth solution. In the scalar case, we show that we can relax the local AR-condition. Finally, for the resonant λ = λ 1 problem, using the nonsmoo...... hiện toàn bộ
On the solution set of an equation of the type f(t, Φ(u(t)) = 0
Set-Valued Analysis - Tập 4 - Trang 399-405 - 1996
Ornella Naselli
We investigate the solution set Γ of an equation of the type f(t, Φ(u(t)) = 0, where Φ is a linear homeomorphism from a topological vector space X onto L 1(T) and f: T×R → R is a Carathéodory function. More precisely, we characterize the property of Γ of intersecting each closed hyperplane of X.
Viability for Differential Inclusions on Graphs
Set-Valued Analysis - Tập 16 - Trang 961-981 - 2008
Mihai Necula, Marius Popescu, Ioan I. Vrabie
Let X be a Banach space, I a nonempty, bounded interval and let $K:I\leadsto X$ be a given multi-valued function. We rephrase the concept of tangent set introduced by Cârjă et al. (Trans Amer Math Soc, 2008; Viability, Invariance and Applications. North-Holland Mathematics Studies, vol. 207. Elsevier, 20...... hiện toàn bộ
Denting points in Köthe-Bochner spaces
Set-Valued Analysis - Tập 2 - Trang 439-458 - 1994
Charles Castaing, Ryszard Pluciennik
A characterization of denting points in the unit ball of Köthe-Bochner spaceE(X) is given. This characterization is a generalization of some analogous theorems for Bochner and Musielak Orlicz spaces and it is compared to similar known results concerning strongly extreme points inE(X).
A Characterization of Maximal Monotone Operators
Set-Valued Analysis - Tập 16 - Trang 693-700 - 2007
Andreas Löhne
It is shown that a set-valued map $M:\mathbb{R}^{q} \rightrightarrows \mathbb{R}^{q}$ is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the norm...... hiện toàn bộ
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