• Corpus ID: 126327315

# Selections and approximations of convex-valued equivariant mappings

```@article{Dzedzej2012SelectionsAA,
title={Selections and approximations of convex-valued equivariant mappings},
author={Zdzisław Dzedzej and W. Kryszewski},
journal={Topological Methods in Nonlinear Analysis},
year={2012},
volume={40},
pages={381-414}
}```
• Published 23 April 2012
• Mathematics
• Topological Methods in Nonlinear Analysis
We present some abstract theorems on the existence of selections and graph-approximations of set-valued mappings with convex values in the equivariant setting, i.e maps commuting with the action of a compact group. Some known results of the Michael, Browder and Cellina type are generalized to this context. The equivariant measurable as well as Caratheodory selection/approximation problems are also studied.
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## References

SHOWING 1-10 OF 32 REFERENCES
Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
• Mathematics
• 1983
Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection
EQUILIBRIA OF SET-VALUED MAPS ON NONCONVEX DOMAINS
• Mathematics
• 1997
We present new theorems on the existence of equilibria (or zeros) of convex as well as nonconvex set-valued maps defined on compact neighborhood retracts of normed spaces. The maps are subject to
ON RELATIVE APPROXIMATION THEOREMS
• Mathematics
• 2002
We consider an approach which reduces the solution of the approximation problem for a USC mapping to an appropriate selection-type restriction of the family of values of this mapping. As a corollary
The fixed point theory of multi-valued mappings in topological vector spaces
Introduction Let K be a compact convex subset of a real topological vector space E, which we shall always assume to be separated (i.e. Hausdorff). We consider multi-valued mappings T of K into E,
Mappings between function spaces
• Mathematics
• 1952
In the following we shall let U = [u] and Q3 = [v] denote arbitrary Banach spaces, and Z = [t] denote a Hausdorff space. X and 2) are to denote the spaces of all continuous functions mapping Z into U
Set-valued analysis
This chapter relates the notions of mutations with the concept of graphical derivatives of set-valued maps and more generally links the above results of morphological analysis with some basic facts
Optimization And Nonsmooth Analysis
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.
Real Analysis
– Weierstrass Theorem Theorem If f is a continuous real-valued function on [a, b] and if any is given, then there exists a polynomial p on [a, b] s.t. |f(x)− p(x)| < for all x ∈ [a, b]. In other
Approximation of set valued functions and fixed point theorems
SommarioIl risultato fondamentale della Nota è il seguente: siaΓ una multiapplicazione semicontinua superiormente da uno spazio metrico compatto S ad uno spazio normato Y, tale cheΓ(x) è convesso.