| Title:
|
Some stability theorems for some iteration processes (English) |
| Author:
|
Imoru, C. O. |
| Author:
|
Olatinwo, M. O. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
81-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we obtain some stability results for Picard and Mann iteration processes in metric space and normed linear space respectively, using two different contractive definitions which are more general than those of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].\par Our results are generalizations of some results of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6]. (English) |
| Keyword:
|
stability results |
| Keyword:
|
Picard and Mann iteration processes |
| MSC:
|
47H06 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47J25 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1138.47046 |
| idMR:
|
MR2321300 |
| . |
| Date available:
|
2009-08-21T07:06:54Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133452 |
| . |
| 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 (2002). Zbl 1212.26040, MR 1995230 |
| Reference:
|
[3] Berinde V.: A priori and A posteriori Error Estimates for a class of $\varphi $-contractions.Bulletins for Applied & Computing Math. (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 Results for Picard and Mann Iteration Procedures.J. Appl. Funct. 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. 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, 2 (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.: 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:
|
[12] Rhoades B. E.: Some Fixed Point Iteration Procedures.Internat. J. Math. and Math. Sci. 14, 1 (1991), 1–16. Zbl 0716.47030, MR 1087396 |
| Reference:
|
[13] Zeidler E.: Nonlinear Functional Analysis, its Applications, Fixed-Point Theorems I. : Springer-Verlag, New York., 1986. MR 0816732 |
| . |
