| Title:
|
On the convergence of the Ishikawa iterates to a common fixed point of two mappings (English) |
| Author:
|
Ćirić, Lj. B. |
| Author:
|
Ume, J. S. |
| Author:
|
Khan, M. S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
123-127 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $C$ be a convex subset of a complete convex metric space $X$, and $S$ and $T$ be two selfmappings on $C$. In this paper it is shown that if the sequence of Ishikawa iterations associated with $S$ and $T$ converges, then its limit point is the common fixed point of $S$ and $T$. This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3]. (English) |
| Keyword:
|
Ishikawa iterates |
| Keyword:
|
comon fixed point |
| Keyword:
|
convex metric space |
| MSC:
|
47H10 |
| MSC:
|
47J25 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1109.47312 |
| idMR:
|
MR1994568 |
| . |
| Date available:
|
2008-06-06T22:41:26Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107858 |
| . |
| Reference:
|
[1] Ćirić, Lj. B.: A generalization of Banach’s contraction principle.Proc. Amer. Math. Soc. 45 (1974), 267–273. MR 0356011 |
| Reference:
|
[2] Ćirić, Lj. B.: Quasi-contractions in Banach spaces.Publ. Inst. Math. 21 (1977), 41–48. MR 0461224 |
| Reference:
|
[3] Hichs, L. and Kubicek, J. D.: On the Mann iteration process in Hilbert spaces.J. Math. Anal. Appl. 59 (1977), 498–504. MR 0513062 |
| Reference:
|
[4] Ishikawa, S.: Fixed points by a new iteration method.Proc. Amer. Math. Soc. 44 (1974), 147–150. Zbl 0286.47036, MR 0336469 |
| Reference:
|
[5] Mann, W. R.: Mean value methods in iteration,.Proc. Amer. Math. Soc. 4 (1953), 506–510. Zbl 0050.11603, MR 0054846 |
| Reference:
|
[6] Naimpally, S. A. and Singh, K. L.: Extensions of some fixed point theorems of Rhoades.J. Math. Anal. Appl. 96 (1983), 437–446. MR 0719327 |
| Reference:
|
[7] Rhoades, B. E.: Fixed point iterations using infinite matrices.Trans. Amer. Math. Soc. 196 (1974), 161–176. Zbl 0422.90089, MR 0348565 |
| Reference:
|
[8] Rhoades, B. E.: A comparison of various definitions of contractive mappings.Trans. Amer. Math. Soc. 226 (1977), 257–290. Zbl 0394.54026, MR 0433430 |
| Reference:
|
[9] Rhoades, B. E.: Extension of some fixed point theorems of Ćirić, Maiti and Pal.Math. Sem. Notes Kobe Univ. 6 (1978), 41–46. MR 0494051 |
| Reference:
|
[10] Rhoades, B. E.: Comments on two fixed point iteration methods.J. Math. Anal. Appl. 56 (1976), 741–750. Zbl 0353.47029, MR 0430880 |
| Reference:
|
[11] Singh, K. L.: Fixed point iteration using infinite matrices.In “Applied Nonlinear Analysis” (V. Lakshmikantham, Ed.), pp.689–703, Academic Press, New York, 1979. MR 0537576 |
| Reference:
|
[12] Singh, K. L.: Generalized contractions and the sequence of iterates.In “Nonlinear Equations in Abstract Spaces” (V. Lakshmikantham, Ed.), pp. 439–462, Academic Press, New York, 1978. MR 0502557 |
| Reference:
|
[13] Takahashi, W.: A convexity in metric spaces and nonexpansive mappings.Kodai Math. Sem. Rep. 22 (1970), 142–149. MR 0267565 |
| . |
