| Autor: |
Theodore Burton, Ioannis Purnaras |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2019, Iss 94, Pp 1-24 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2019.1.94 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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