| Title:
|
A remark on the minimal displacement problem in spaces uniformly rotund in every direction (English) |
| Author:
|
Bolibok, Krzysztof |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
85-90 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give an example of uniformly rotund in every direction space for which the minimal displacement characteristic is maximal. (English) |
| Keyword:
|
Lipschitzian mappings |
| Keyword:
|
minimal displacement |
| MSC:
|
46B20 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1100.47513 |
| idMR:
|
MR2045847 |
| . |
| Date available:
|
2009-01-08T19:27:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119369 |
| . |
| Reference:
|
[1] Benyamini Y., Sternfeld Y.: Spheres in infinite dimensional normed spaces are Lipschitz contractible.Proc. Amer. Math. Soc. 88 (1983), 439-445. Zbl 0518.46010, MR 0699410 |
| Reference:
|
[2] Bolibok K.: Constructions of Lipschitzian mappings with non zero minimal displacement in spaces $L^{1}(0,1)$ and $L^{2}(0,1)$.Annal. Univ. Marie Curie-Sklodowska L (1996), 25-31. MR 1472574 |
| Reference:
|
[3] Bolibok K.: Minimal displacement and retraction problems in the space $l^{1}$.Nonlinear Analysis Forum 3 (1998), 13-23. MR 1646488 |
| Reference:
|
[4] Bolibok K., Goebel K.: A note on minimal displacement and retraction problems.J. Math. Anal. Appl. 206 (1997), 308-314. Zbl 0883.47066, MR 1429293 |
| Reference:
|
[5] Goebel K.: On the minimal displacement of points under Lipschitzian mappings.Pacific J. Math. 48 (1973), 151-163. Zbl 0265.47046, MR 0328708 |
| Reference:
|
[6] Goebel K., Kirk W.A.: Topics in Metric Fixed Point Theory.Cambridge University Press, Cambridge, 1990. MR 1074005 |
| Reference:
|
[7] Lin P.K., Sternfeld Y.: Convex sets with the Lipschitz fixed point property are compact Proc. Amer. Math. Soc..93 (1985), 633-639. MR 0776193 |
| Reference:
|
[8] Schauder J.: Der Fixpunktsatz in Funkionalraumen.Studia Math. 2 (1930), 171-180. |
| Reference:
|
[9] Zizler V.: On some rotundity and smoothness properties of Banach spaces.Rozprawy Mat. 87 (1971). Zbl 0231.46036, MR 0300060 |
| . |
