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...
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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 |
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| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2019.1.94 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Burton Theodore A. | |
| 245 | 1 | 0 | |a Necessary and sufficient conditions for large contractions in fixed point theory |h [elektronikus dokumentum] / |c Burton Theodore A. |
| 260 | |c 2019 | ||
| 300 | |a 1-24 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a 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. | |
| 695 | |a Differenciaegyenlet, Integrálegyenlet | ||
| 700 | 0 | 1 | |a Purnaras Ioannis K. |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/66361/1/ejqtde_2019_094.pdf |z Dokumentum-elérés |