| Title:
|
Fixed point theorems for $n$-periodic mappings in Banach spaces (English) |
| Author:
|
Górnicki, Jarosław |
| Author:
|
Pupka, Krzysztof |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
33-42 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. {\bf 29} (1971), 294) and others, which have recently been presented in Chapter 11 of {\it Handbook of Metric Fixed Point Theory\/} (2001). (English) |
| Keyword:
|
lipchitzian mapping |
| Keyword:
|
uniformly lipschitzian mapping |
| Keyword:
|
$n$-periodic mapping |
| Keyword:
|
fixed point |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1123.47038 |
| idMR:
|
MR2175857 |
| . |
| Date available:
|
2009-05-05T16:49:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119506 |
| . |
| Reference:
|
[1] Goebel K.: Convexity of balls and fixed point theorems for mappings with nonexpansive square.Compositio Math. 22 (1970), 269-274. Zbl 0202.12802, MR 0273477 |
| Reference:
|
[2] Goebel K., Kirk W.A.: A fixed point theorem for transformations whose iterates have uniform Lipschitz constant.Studia Math. 47 (1973), 135-140. Zbl 0265.47044, MR 0336468 |
| Reference:
|
[3] Goebel K., Złotkiewicz E.: Some fixed point theorems in Banach spaces.Colloquium Math. 23 (1971), 103-106. MR 0303367 |
| Reference:
|
[4] Górnicki J.: Fixed points of involutions.Math. Japonica 43 1 (1996), 151-155. MR 1373993 |
| Reference:
|
[5] Halpern B.: Fixed points of nonexpansive maps.Bull. Amer. Math. Soc. 73 (1967), 957-961. MR 0218938 |
| Reference:
|
[6] Kim T.H., Kirk W.A.: Fixed point theorems for lipschitzian mappings in Banach spaces.Nonlinear Anal. 26 (1996), 1905-1911. Zbl 0856.47031, MR 1386122 |
| Reference:
|
[7] Kirk W.A.: A fixed point theorem for mappings with a nonexpansive iterate.Proc. Amer. Math. Soc. 29 (1971), 294-298. Zbl 0213.41303, MR 0284887 |
| Reference:
|
[8] Kirk W.A., Sims B. (Eds.): Handbook of Metric Fixed Point Theory.Kluwer Acad. Pub., Dordrecht-Boston-London, 2001. Zbl 0970.54001, MR 1904271 |
| Reference:
|
[9] Linhart J.: Fixpunkte von Involutionen n-ter Ordnung.Österreich. Akad., Wiss. Math.-Natur., kl. II, 180 (1973), 89-93. Zbl 0244.47041, MR 0303369 |
| . |
