A fixed point theorem for contraction mappings
Let S be a closed subset of a Banach space E and f:S→E be a strict contraction mapping. Suppose there exists a mapping h:S→(0,1] such that (1−h(x))x+h(x)f(x)∈S for each x∈S. Then for any x0∈S, the sequence {xn} in S defined by xn+1=(1−h(xn))xn+h(xn)f(xn), n≥0, converges to a u∈S. Further, if ∑h(xn)=...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000271 |