Set-Valued Analysis

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Continuous Selections and Finite C-Spaces
Set-Valued Analysis - - 2002
Vesko Valov
Characterization of paracompact finite C-spaces via continuous selections avoiding Z σ-sets are given. We apply these results to obtain some properties of finite C-spaces. Factorization theorems and a completion theorem for finite C-spaces are also proved.
On Attractors of Multivalued Semi-Flows and Differential Inclusions
Set-Valued Analysis - Tập 6 - Trang 83-111 - 1998
Valery S. Melnik, José Valero
In this paper we study the existence of global attractors for multivalued dynamical systems. These theorems are then applied to dynamical systems generated by differential inclusions for which the solution is not unique for a given initial state. Finally, some boundary-value problems are considered.
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
Gap Continuity of Multimaps
Set-Valued Analysis - Tập 16 - Trang 429-442 - 2007
Jean-Paul Penot
We introduce a notion of continuity for multimaps (or set-valued maps) which is mild. It encompasses both lower semicontinuity and upper semicontinuity. We give characterizations and we consider some permanence properties. This notion can be used for various purposes. In particular, it is used for continuity properties of subdifferentials and of value functions in parametrized optimization problem...... hiện toàn bộ
Eigenvalues of Set-Valued Operators in Banach Spaces
Set-Valued Analysis - Tập 13 Số 1 - Trang 1-19 - 2005
Rafaël Correa, Pedro Gajardo
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
Rapid Growth Paths in Multivalued Dynamical Systems Generated by Homogeneous Convex Stochastic Operators
Set-Valued Analysis - Tập 6 - Trang 61-81 - 1998
I. V. Evstigneev, S. D. Flå m
The paper examines dynamical systems generated by convex homogeneous multivalued operators in spaces of random vectors. The primary goal is to investigate the growth rates of random trajectories of these dynamical systems. Existence and characterization theorems for ‘rapid’ trajectories, growing faster in a certain sense than others, are obtained.
Linear Monotone Subspaces of Locally Convex Spaces
Set-Valued Analysis - Tập 18 - Trang 29-55 - 2009
M. D. Voisei, C. Zălinescu
The main focus of this paper is to study multi-valued linear monotone operators in the context of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness, negative-infimum, and (dual-)representability are studied and criteria are provided.
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
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