| Title:
|
Convergence Results for Jungck-type Iterative Processes in Convex Metric Spaces (English) |
| Author:
|
Olatinwo, Memudu Olaposi |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
79-87 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the convergence results of [V. Berinde; A convergence theorem for Mann iteration in the class of Zamfirescu operators, Analele Universitatii de Vest, Timisoara, Seria Matematica-Informatica 45 (1) (2007), 33–41], [V. Berinde; On the convergence of Mann iteration for a class of quasi-contractive operators, Preprint, North University of Baia Mare (2003)] and [V. Berinde; On the Convergence of the Ishikawa Iteration in the Class of Quasi-contractive Operators, Acta Math. Univ. Comenianae 73 (1) (2004), 119–126] are extended from arbitrary Banach space setting to the convex metric space by weakening further the conditions on the parameter sequence $\lbrace \alpha _n\rbrace \subset [0,1]$. We establish the convergence of Jungck–Mann and Jungck–Ishikawa iterative processes for two nonselfmappings in a convex metric space setting by employing a general contractive condition. Similar results are also deduced for the Mann and Ishikawa iterations. Our results generalize, extend and improve a multitude of results in the literature including those of Berinde mentioned above. (English) |
| Keyword:
|
arbitrary Banach space setting |
| Keyword:
|
Jungck–Mann and Jungck–Ishikawa iterative processes |
| Keyword:
|
convex metric space |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 06204922 |
| idMR:
|
MR3060010 |
| . |
| Date available:
|
2012-06-25T08:24:57Z |
| Last updated:
|
2014-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142875 |
| . |
| Reference:
|
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