| Title:
|
On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces (English) |
| Author:
|
Bosede, Alfred Olufemi |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
17-22 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others. (English) |
| Keyword:
|
stability |
| Keyword:
|
nonselfmappings |
| Keyword:
|
Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1263.47076 |
| idMR:
|
MR2920695 |
| . |
| Date available:
|
2011-12-08T09:44:05Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141715 |
| . |
| Reference:
|
[1] Berinde, V.: On stability of some fixed point procedures. Bul. Śtiint. Univ. Baia Mare, Ser. B, Mathematică–Informatică 17, 1 (2002), 7–14. MR 2014277 |
| Reference:
|
[2] Berinde, V.: Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare, 2002. Zbl 1036.47037, MR 1995230 |
| Reference:
|
[3] Bosede, A. O.: Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces. Fasciculi Mathematici 42 (2009), 29–38. Zbl 1178.47042, MR 2573523 |
| Reference:
|
[4] Bosede, A. O.: Some common fixed point theorems in normed linear spaces. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 49, 1 (2010), 19–26. MR 2797519 |
| Reference:
|
[5] Bosede, A. O.: Strong convergence results for the Jungck-Ishikawa and Jungck-Mann iteration processes. Bulletin of Mathematical Analysis and Applications 2, 3 (2010), 65–73. MR 2718198 |
| Reference:
|
[6] Bosede, A. O., Rhoades, B. E.: Stability of Picard and Mann iterations for a general class of functions. Journal of Advanced Mathematical Studies 3, 2 (2010), 1–3. MR 2722440 |
| Reference:
|
[7] Harder, A. M., Hicks, T. L.: Stability results for fixed point iteration procedures. Math. Japonica 33 (1988), 693–706. Zbl 0655.47045, MR 0972379 |
| Reference:
|
[8] Imoru, C. O., Olatinwo, M. O.: Some stability theorems for some iteration processes. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 45 (2006), 81–88. Zbl 1138.47046, MR 2321300 |
| Reference:
|
[9] Ishikawa, S.: Fixed points by a new iteration method. Proc. Amer. Math. Soc. 44 (1974), 147–150. Zbl 0286.47036, MR 0336469, 10.1090/S0002-9939-1974-0336469-5 |
| Reference:
|
[10] Jungck, G.: Commuting mappings and fixed points. Amer. Math. Monthly 83 (1976), 261–263. Zbl 0321.54025, MR 0400196, 10.2307/2318216 |
| Reference:
|
[11] Krasnoselskij, M. A.: Two remarks on the method of successive approximations. Uspehi Mat. Nauk. 10, 1 (1955), 123–127 (in Russian). MR 0068119 |
| Reference:
|
[12] Mann, W. R.: Mean value methods in iterations. Proc. Amer. Math. Soc. 4 (1953), 506–510. MR 0054846, 10.1090/S0002-9939-1953-0054846-3 |
| Reference:
|
[13] Olatinwo, M. O.: Some stability and strong convergence results for the Jungck–Ishikawa iteration process. Creat. Math. Inform. 17 (2008), 33–42. Zbl 1199.47282, MR 2409230 |
| Reference:
|
[14] 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:
|
[15] Singh, S. L., Bhatmagar, C., Mishra, S. N.: Stability of Jungck-type iterative procedures. International J. Math. & Math. Sc. 19 (2005), 3035–3043. MR 2206082, 10.1155/IJMMS.2005.3035 |
| . |
