| Title:
|
Singularities and equicontinuity of certain families of set-valued mappings (English) |
| Author:
|
Trif, Tiberiu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
353-365 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex processes is derived. This principle immediately yields the uniform boundedness theorem stated in [1, Theorem 2.3.1]. (English) |
| Keyword:
|
condensation of the singularities |
| Keyword:
|
equicontinuity |
| Keyword:
|
generalized convex set-valued mappings |
| Keyword:
|
closed convex processes |
| MSC:
|
26B25 |
| MSC:
|
46N10 |
| MSC:
|
54C60 |
| idZBL:
|
Zbl 0937.46064 |
| idMR:
|
MR1651971 |
| . |
| Date available:
|
2009-01-08T18:41:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119012 |
| . |
| Reference:
|
[1] Aubin J.P., Frankowska H.: Set-Valued Analysis.Birkhäuser Boston (1990). Zbl 0713.49021, MR 1048347 |
| Reference:
|
[2] Breckner W.W.: Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer Funktionen in topologischen linearen Räumen.Publ. Inst. Math. (Beograd) 23 (37) (1978), 13-20. Zbl 0416.46029, MR 0508122 |
| Reference:
|
[3] Breckner W.W.: A principle of condensation of singularities for set-valued functions.Mathematica-Rev. Anal. Numér. Théor. Approx., Sér. L'Anal. Numér. Théor. Approx. 12 (1983), 101-111. Zbl 0527.54015, MR 0743128 |
| Reference:
|
[4] Breckner W.W.: Continuity of generalized convex and generalized concave set-valued functions.Rev. Anal. Numér. Théor. Approx. 22 (1993), 39-51. Zbl 0799.54016, MR 1621546 |
| Reference:
|
[5] Breckner W.W., Trif T.: On the singularities of certain families of nonlinear mappings.Pure Math. Appl. 6 (1995), 121-137. Zbl 0852.47034, MR 1430264 |
| . |
