Continuous selections and approximations in α-convex metric spaces

A. Kowalska

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 2, page 265-294
  • ISSN: 1509-9407

Abstract

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In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.

How to cite

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A. Kowalska. "Continuous selections and approximations in α-convex metric spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.2 (2007): 265-294. <http://eudml.org/doc/271154>.

@article{A2007,
abstract = {In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.},
author = {A. Kowalska},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {generalized convexity; selections; relative selections; graph-approximations},
language = {eng},
number = {2},
pages = {265-294},
title = {Continuous selections and approximations in α-convex metric spaces},
url = {http://eudml.org/doc/271154},
volume = {27},
year = {2007},
}

TY - JOUR
AU - A. Kowalska
TI - Continuous selections and approximations in α-convex metric spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 2
SP - 265
EP - 294
AB - In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
LA - eng
KW - generalized convexity; selections; relative selections; graph-approximations
UR - http://eudml.org/doc/271154
ER -

References

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  13. [13] W. Kryszewski, Graph-approximation of set-valued maps. A survey, Non. Anal. 2 (1998), 223-235. Zbl1086.54500
  14. [14] W. Kryszewski, Graph-approximation of set-valued maps on noncompact domains, Topology & Appl. 83 (1988), 1-21. Zbl0933.54023
  15. [15] E. Michael, Continuous selections I, Ann. of Math. 63 (2) (1956), 361-382. Zbl0071.15902
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