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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |