| Title:
|
Some stability results in complete metric space (English) |
| Author:
|
Olatinwo, Memudu Olaposi |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
83-92 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we obtain some stability results for the Picard iteration process for one and two metrics in complete metric space by using different contractive definitions which are more general than those of Berinde [Berinde, V.: On the stability of some fixed point procedures. Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica–Informatica 18, 1 (2002), 7–14.], Imoru and Olatinwo [Imoru, C. O., Olatinwo, M. O.: On the stability of Picard and Mann iteration processes. Carpathian J. Math. 19, 2 (2003), 155–160.] some others listed in the reference section. The results generalize and unify some of the results of Harder and Hicks [Harder, A. M., Hicks, T. L.: Stability results for fixed point iteration procedures. Math. Japonica 33, 5 (1988), 693–706.], Rhoades [Rhoades, B. E.: Fixed point theorems and stability results for fixed point iteration procedures. Indian J. Pure Appl. Math. 21, 1 (1990), 1–9.], [Rhoades, B. E.: Fixed point theorems and stability results for fixed point iteration procedures II. Indian J. Pure Appl. Math. 24, 11 (1993), 691–703.], Osilike [Osilike, M. O.: Some stability results for fixed point iteration procedures. J. Nigerian Math. Soc. Vol. 14/15 (1995), 17–29.], Berinde [Berinde, V.: On the stability of some fixed point procedures. Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica–Informatica 18, 1 (2002), 7–14.], Imoru and Olatinwo [Imoru, C. O., Olatinwo, M. O.: On the stability of Picard and Mann iteration processes. Carpathian J. Math. 19, 2 (2003), 155–160.] as well as Imoru et al [Imoru, C. O., Olatinwo, M. O., Owojori, O. O.: On the stability of Picard and Mann iteration procedures. J. Appl. Func. Diff. Eqns. 1, 1 (2006), 71–80.]. (English) |
| Keyword:
|
Stability results |
| Keyword:
|
Picard and Mann iteration processes |
| MSC:
|
47H06 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1199.54232 |
| idMR:
|
MR2641950 |
| . |
| Date available:
|
2010-02-11T13:56:49Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137516 |
| . |
| Reference:
|
[1] Berinde, V.: On the stability of some fixed point procedures.Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica–Informatica 18, 1 (2002), 7–14. Zbl 1031.47030, MR 2014277 |
| Reference:
|
[2] Berinde, V.: Iterative Approximation of Fixed Points.Editura Efemeride, Baia Mare, Romania, 2002. Zbl 1036.47037, MR 1995230 |
| Reference:
|
[3] Berinde, V.: A priori and a posteriori error estimates for a class of $\varphi $-contractions.Bulletins for Applied Mathematics 90-B (1999), 183–192. |
| Reference:
|
[4] Harder, A. M., Hicks, T. L.: Stability results for fixed point iteration procedures.Math. Japonica 33, 5 (1988), 693–706. Zbl 0655.47045, MR 0972379 |
| Reference:
|
[5] Imoru, C. O., Olatinwo, M. O.: On the stability of Picard and Mann iteration processes.Carpathian J. Math. 19, 2 (2003), 155–160. Zbl 1086.47512, MR 2069844 |
| Reference:
|
[6] Imoru, C. O., Olatinwo, M. O., Owojori, O. O.: On the stability of Picard and Mann iteration procedures.J. Appl. Func. Diff. Eqns. 1, 1 (2006), 71–80. MR 2293939 |
| Reference:
|
[7] Jachymski, J. R.: An extension of A. Ostrowski’s theorem on the round-off stability of iterations.Aequationes Math. 53 (1997), 242–253. Zbl 0885.47023, MR 1444177 |
| Reference:
|
[8] Osilike, M. O.: Some stability results for fixed point iteration procedures.J. Nigerian Math. Soc. Vol. 14/15 (1995), 17–29. MR 1775011 |
| Reference:
|
[9] Osilike, M. O., Udomene, A.: Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings.Indian J. Pure Appl. Math. 30, 12 (1999), 1229–1234. Zbl 0955.47038, MR 1729212 |
| Reference:
|
[10] Rhoades, B. E.: Fixed point theorems and stability results for fixed point iteration procedures.. Indian J. Pure Appl. Math. 21, 1 (1990), 1–9. Zbl 0692.54027, MR 1048010 |
| Reference:
|
[11] Rhoades, B. E.: Some fixed point iteration procedures.Internat. J. Math. and Math. Sci. 14, 1 (1991), 1–16. Zbl 0716.47030 |
| Reference:
|
[12] Rhoades, B. E.: Fixed point theorems and stability results for fixed point iteration procedures II.Indian J. Pure Appl. Math. 24, 11 (1993), 691–703. Zbl 0794.54048, MR 1251180 |
| Reference:
|
[13] Singh, S. L., Bhatnagar, C., Mishra, S. N.: Stability of Jungck-type iterative procedures.Internat. J. Math. & Math. Sc. 19 (2005), 3035–3043. Zbl 1117.26005, MR 2206082 |
| Reference:
|
[14] Zeidler, E.: Nonlinear Functional Analysis and its Applications, Fixed-Point Theorems I.Springer-Verlag, New York, 1986. MR 0816732 |
| . |
