On Series-Like Iterative Equation with a General Boundary Restriction
By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation 𝒫(f)∘f=F. Moreover, we get that the solution f depends continuously on F. As a corollary, we investigate the existence...
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| Format: | Article |
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SpringerOpen
2009-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/892691 |
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doaj-429d846bf2694f9c806118eab8398ce92020-11-25T00:21:43ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-01200910.1155/2009/892691On Series-Like Iterative Equation with a General Boundary RestrictionWei SongGuo-qiu YangFeng-chun LeiBy means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation 𝒫(f)∘f=F. Moreover, we get that the solution f depends continuously on F. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation ∑n=1∞anfn(x)=F(x),  x∈𝔹 with a general boundary restriction, where F:𝔹→𝔸 is a given Lipschitz function, and 𝔹,𝔸 are compact convex subsets of ℝN with nonempty interior. http://dx.doi.org/10.1155/2009/892691 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wei Song Guo-qiu Yang Feng-chun Lei |
| spellingShingle |
Wei Song Guo-qiu Yang Feng-chun Lei On Series-Like Iterative Equation with a General Boundary Restriction Fixed Point Theory and Applications |
| author_facet |
Wei Song Guo-qiu Yang Feng-chun Lei |
| author_sort |
Wei Song |
| title |
On Series-Like Iterative Equation with a General Boundary Restriction |
| title_short |
On Series-Like Iterative Equation with a General Boundary Restriction |
| title_full |
On Series-Like Iterative Equation with a General Boundary Restriction |
| title_fullStr |
On Series-Like Iterative Equation with a General Boundary Restriction |
| title_full_unstemmed |
On Series-Like Iterative Equation with a General Boundary Restriction |
| title_sort |
on series-like iterative equation with a general boundary restriction |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2009-01-01 |
| description |
By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation 𝒫(f)∘f=F. Moreover, we get that the solution f depends continuously on F. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation ∑n=1∞anfn(x)=F(x),  x∈𝔹 with a general boundary restriction, where F:𝔹→𝔸 is a given Lipschitz function, and 𝔹,𝔸 are compact convex subsets of ℝN with nonempty interior. |
| url |
http://dx.doi.org/10.1155/2009/892691 |
| work_keys_str_mv |
AT weisong onserieslikeiterativeequationwithageneralboundaryrestriction AT guoqiuyang onserieslikeiterativeequationwithageneralboundaryrestriction AT fengchunlei onserieslikeiterativeequationwithageneralboundaryrestriction |
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1716182123473272832 |