A pointwise contraction criteria for the existence of fixed points
Let S be a subset of a metric space (X,d) and T:S→X be a mapping. In this paper, we define the notion of lower directional increment QT(x,y] of T at x∈S in the direction of y∈X and give sufficient conditions for T to have a fixed point when QT(x,Tx]<1 for each x∈S. The results herein generalize t...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000363 |
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| Summary: | Let S be a subset of a metric space (X,d) and T:S→X be a mapping. In this paper, we define the notion of lower directional increment QT(x,y] of T at x∈S in the direction of y∈X and give sufficient conditions for T to have a fixed point when QT(x,Tx]<1 for each x∈S. The results herein generalize the recent theorems of Clarke (Caned. Math. Bull. Vol. 21(1), 1978, 7-11) and also improve considerably some earlier results. |
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| ISSN: | 0161-1712 1687-0425 |