Name
Abstract | ||
|---|---|---|
For any upper semicontinuous and compact-valued (usco) mapping F : X → Y from a metric space X without isolated points into a normed space Y, we prove the existence of a single-valued continuous mapping f : X → Y such that the Hausdorff distance between graphs ΓF and Γf is arbitrarily small, whenever "measure of nonconvexity" of values of F admits an appropriate common upper estimate. Hence, we prove a version of the Beer-Cellina theorem, under controlled withdrawal of convexity of values of multifunctions. We also give conditions for such strong approximability of star-shaped-valued upper semicontinuous (usc) multifunctions in comparison with Beer's result for Hausdorff continuous star-shaped-valued multifunctions. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jath.2002.3707 | Journal of Approximation Theory |
Keywords | DocType | Volume |
upper semicontinuous,strong approximation,Hausdorff distance,hausdorff distance.,single-valued continuous mapping,function of nonconvexity,metric space X,mapping F,normed space Y,star-shaped-valued upper semicontinuous,selection,appropriate common upper estimate,Beer-Cellina theorem,Hausdorff continuous star-shaped-valued multifunctions,USC nonconvex-valued mapping,approximation,paraconvexity,multivalued mapping | Journal | 119 |
Issue | ISSN | Citations |
1 | 0021-9045 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dusan Repovš | 1 | 21 | 11.09 |
| Pavel V. Semenov | 2 | 0 | 0.34 |