| Title:
|
Convergence of approximating fixed points sets for multivalued nonexpansive mappings (English) |
| Author:
|
Pietramala, Paolamaria |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
697-701 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K$ be a closed convex subset of a Hilbert space $H$ and $T:K \multimap K$ a nonexpansive multivalued map with a unique fixed point $z$ such that $\{z\}=T(z)$. It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to $z$. (English) |
| Keyword:
|
multivalued nonexpansive map |
| Keyword:
|
fixed points set |
| Keyword:
|
Mosco convergence |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 0756.47039 |
| idMR:
|
MR1159816 |
| . |
| Date available:
|
2009-01-08T17:48:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118449 |
| . |
| Reference:
|
[1] Browder F.E.: Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces.Arch. Rational. Mech. Anal. 24 (1967), 82-90. Zbl 0148.13601, MR 0206765 |
| Reference:
|
[2] Reich S.: Strong convergence theorems for resolvents of accretive operators in Banach spaces.J. Math. Anal. Appl. 75 (1980), 287-292. Zbl 0437.47047, MR 0576291 |
| Reference:
|
[3] Singh S.P., Watson B.: On approximating fixed points.Proc. Symp. Pure Math. 45 (part 2) (1986), 393-395. Zbl 0597.47035, MR 0843624 |
| Reference:
|
[4] Reich S.: Fixed points of contractive functions.Boll. UMI 5 (1972), 26-42. Zbl 0249.54026, MR 0309095 |
| Reference:
|
[5] Ćirić L.B.: Fixed points for generalized multivalued contractions.Mat. Vesnik, N. Ser. 9 {(24)} (1972), 265-272. MR 0341460 |
| Reference:
|
[6] Iséki K.: Multivalued contraction mappings in complete metric spaces.Math. Sem. Notes 2 (1974), 45-49. MR 0413070 |
| Reference:
|
[7] Corley H.W.: Some hybrid fixed point theorems related to optimization.J. Math. Anal. Appl. 120 (1986), 528-532. Zbl 0631.47041, MR 0864769 |
| Reference:
|
[8] LamiDozo E.: Multivalued nonexpansive mappings and Opial's condition.Proc. Amer. Math. Soc. 38 (1973), 286-292. MR 0310718 |
| . |
