Set-Valued Analysis
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Continuous Selections and Finite C-Spaces
Set-Valued Analysis - - 2002
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
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
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...
Gap Continuity of Multimaps
Set-Valued Analysis - Tập 16 - Trang 429-442 - 2007
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...
Eigenvalues of Set-Valued Operators in Banach Spaces
Set-Valued Analysis - Tập 13 Số 1 - Trang 1-19 - 2005
Comparative Properties of Three Metrics in the Space of Compact Convex Sets
Set-Valued Analysis - Tập 5 - Trang 267-289 - 1997
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...
Rapid Growth Paths in Multivalued Dynamical Systems Generated by Homogeneous Convex Stochastic Operators
Set-Valued Analysis - Tập 6 - Trang 61-81 - 1998
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
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
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...
Hyperspaces of Banach Spaces with the Attouch—Wets Topology
Set-Valued Analysis - Tập 12 - Trang 329-344 - 2004
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 (X) consisting of finite sets, compact sets and bounded closed sets,
respectively. In this paper, it is proved that Fin AW (X)≈Comp AW (X)≈ℓ2(τ)×ℓ2 f
ℓandℓBdd AW...
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