Necessary and sufficient conditions for large contractions in fixed point theory
Many problems in integral and differential equations involve an equation in which there is almost a contraction mapping. Through some type of transformation we arrive at an operator of the form H(x) = x − f(x). The paper contains two main parts. First we offer several transformations which yield tha...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciaegyenlet, Integrálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.94 |
| Online Access: | http://acta.bibl.u-szeged.hu/66361 |
| Tartalmi kivonat: | Many problems in integral and differential equations involve an equation in which there is almost a contraction mapping. Through some type of transformation we arrive at an operator of the form H(x) = x − f(x). The paper contains two main parts. First we offer several transformations which yield that operator. We then offer necessary and sufficient conditions to ensure that the operator is a large contraction. These operators yield unique fixed points. A partial answer to a question raised in [D. R. Smart, Fixed point theorems, Cambridge University Press, Cambridge, 1980] is given. The last section contains examples and applications. |
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| Terjedelem/Fizikai jellemzők: | 1-24 |
| ISSN: | 1417-3875 |