Fixed Point Theorems in Cone Banach Spaces
In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ∥x∥P=d(x,0), if there exist a, b, s and T:C→C satisfies the...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/609281 |
| Summary: | In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ∥x∥P=d(x,0), if there exist a, b, s and T:C→C satisfies the conditions 0≤s+|a|−2b<2(a+b) and 4ad(Tx,Ty)+b(d(x,Tx)+d(y,Ty))≤sd(x,y) for all x,y∈C , then T has at least one Fixed point. |
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| ISSN: | 1687-1820 1687-1812 |