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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/892691 |
| Summary: | 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. |
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| ISSN: | 1687-1820 1687-1812 |