On a General Contractive Condition for Cyclic Self-Mappings
This paper is concerned with 𝑝(≥2)-cyclic self-mappings 𝑇∶⋃𝑖∈𝑝𝐴𝑖→⋃𝑖∈𝑝𝐴𝑖 in a metric space (𝑋, 𝑑), with 𝐴𝑖⊂𝑋, 𝑇(𝐴𝑖)⊆𝐴𝑖+1 for 𝑖=1,2,…,𝑝, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed point...
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Hindawi Limited
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/542941 |
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doaj-1594b44f5760444ea1a7b8dfcbc4a2f02020-11-24T23:00:40ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/542941542941On a General Contractive Condition for Cyclic Self-MappingsM. De la Sen0Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Campus de Leioa (Bizkaia), Apartado 644 de Bilbao, 48080 Bilbao, SpainThis paper is concerned with 𝑝(≥2)-cyclic self-mappings 𝑇∶⋃𝑖∈𝑝𝐴𝑖→⋃𝑖∈𝑝𝐴𝑖 in a metric space (𝑋, 𝑑), with 𝐴𝑖⊂𝑋, 𝑇(𝐴𝑖)⊆𝐴𝑖+1 for 𝑖=1,2,…,𝑝, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed points and best proximity points is discussed as well as the convergence to them of the iterates generated by the self-mapping from given initial points.http://dx.doi.org/10.1155/2011/542941 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. De la Sen |
| spellingShingle |
M. De la Sen On a General Contractive Condition for Cyclic Self-Mappings Journal of Applied Mathematics |
| author_facet |
M. De la Sen |
| author_sort |
M. De la Sen |
| title |
On a General Contractive Condition for Cyclic Self-Mappings |
| title_short |
On a General Contractive Condition for Cyclic Self-Mappings |
| title_full |
On a General Contractive Condition for Cyclic Self-Mappings |
| title_fullStr |
On a General Contractive Condition for Cyclic Self-Mappings |
| title_full_unstemmed |
On a General Contractive Condition for Cyclic Self-Mappings |
| title_sort |
on a general contractive condition for cyclic self-mappings |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2011-01-01 |
| description |
This paper is concerned with 𝑝(≥2)-cyclic self-mappings 𝑇∶⋃𝑖∈𝑝𝐴𝑖→⋃𝑖∈𝑝𝐴𝑖 in a metric space (𝑋, 𝑑), with 𝐴𝑖⊂𝑋, 𝑇(𝐴𝑖)⊆𝐴𝑖+1 for 𝑖=1,2,…,𝑝, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed points and best proximity points is discussed as well as the convergence to them of the iterates generated by the self-mapping from given initial points. |
| url |
http://dx.doi.org/10.1155/2011/542941 |
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AT mdelasen onageneralcontractiveconditionforcyclicselfmappings |
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