| Title:
|
An iteration process for nonlinear mappings in uniformly convex linear metric spaces (English) |
| Author:
|
Beg, Ismat |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
405-412 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We obtain necessary conditions for convergence of the Cauchy Picard sequence of iterations for Tricomi mappings defined on a uniformly convex linear complete metric space. (English) |
| Keyword:
|
linear metric space |
| Keyword:
|
fixed point |
| Keyword:
|
uniformly convex |
| MSC:
|
47H10 |
| MSC:
|
47J25 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1030.47051 |
| idMR:
|
MR1983461 |
| . |
| Date available:
|
2009-09-24T11:02:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127809 |
| . |
| Reference:
|
[1] B. Beauzamy: Un cas de convergence des iterees d’une contraction dans un espace uniforment convexe.(1978), Unpublished. |
| Reference:
|
[2] I. Beg: Structure of the set of fixed points of nonexpansive mappings on convex metric spaces.Annales Univ. Marie Curie-Sklodowska (Sec. A)—Mathematica LII(2)(1), 1998, pp. 7–14. Zbl 1004.54031, MR 1728052 |
| Reference:
|
[3] I. Beg: Inequalities in metric spaces with applications.Topol. Methods Nonlinear Anal. 17 (2001), 183–190. Zbl 0998.47040, MR 1846986, 10.12775/TMNA.2001.012 |
| Reference:
|
[4] I. Beg, A. Azam, F. Ali and T. Minhas: Some fixed point theorems in convex metric spaces.Rend. Circ. Mat. Palermo XL (1991), 307–315. MR 1151591 |
| Reference:
|
[5] I. Beg, N. Shahzad and M. Iqbal: Fixed point theorems and best approximation in convex rmetric spaces.J. Approx. Theory 8 (1992), 97–105. MR 1212852 |
| Reference:
|
[6] L. Ciric: On some discontinuous fixed point theorems in convex metric spaces.Czechoslovak Math. J. 43(188) (1993), 319–326. MR 1211753 |
| Reference:
|
[7] X. P. Ding: Iteration processes for nonlinear mappings in convex metric spaces.J. Math. Anal. Appl. 132 (1988), 114–122. Zbl 0683.47044, MR 0942358, 10.1016/0022-247X(88)90047-9 |
| Reference:
|
[8] L. Gajic and M. Stojakovic: A remark on Kaneko report on general contractive type conditions for multivalued mappings in Takahashi convex metric spaces.Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 23 (1993), 61–66. MR 1333534 |
| Reference:
|
[9] M. D. Guay, K. L. Singh and J. H. M. Whitfield: Fixed point theorems for nonexpansive mappings in convex metric spaces.Nonlinear analysis and application, Proc. int. Conf. Lecture Notes Pure Appl. Math. 80, S. P. Singh, J. H. Barry (eds.), Marcel Dekker Inc., New York, 1982, pp. 179–189. MR 0689554 |
| Reference:
|
[10] W. A. Kirk: Krasnoselskii’s iteration process in hyperbolic spaces.Numer. Funct. Anal. Optim. 4 (1982), 371–381. MR 0673318, 10.1080/01630568208816123 |
| Reference:
|
[10] J. Moreau: Un cos des convergence des iterees d’une contraction d’une espace Hilbertien.C. R. Acad. Paris 286 (1978), 143–144. |
| Reference:
|
[11] S. A. Naimpally, K. L. Singh and J. H. M. Whitfield: Fixed points in convex metric spaces.Math. Japon. 29 (1984), 585–597. MR 0759448 |
| Reference:
|
[12] T. Shimizu and W. Takahashi: Fixed point theorems in certain convex metric spaces.Math. Japon. 37 (1992), 855–859. MR 1186552 |
| Reference:
|
[13] T. Shimizu and W. Takahashi: Fixed points of multivalued mappings in certain convex metric spaces.Topol. Methods Nonlinear Anal. 8 (1996), 197–203. MR 1485764, 10.12775/TMNA.1996.028 |
| Reference:
|
[14] W. Takahashi: A convexity in metric spaces and nonexpansive mapping I.Kodai Math. Sem. Rep. 22 (1970), 142–149. MR 0267565, 10.2996/kmj/1138846111 |
| Reference:
|
[15] F. Tricomi: Una teorema sulla convergenza delle successioni formate delle successive iterate di una funzione di una variabile reale.Giorn. Mat. Bataglini 54 (1916), 1–9. |
| . |
