Burton Theodore A. and Purnaras Ioannis K.: Necessary and sufficient conditions for large contractions in fixed point theory. (2019)
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Abstract
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.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2019 |
| Number: | 94 |
| ISSN: | 1417-3875 |
| Page Range: | pp. 1-24 |
| DOI: | 10.14232/ejqtde.2019.1.94 |
| Uncontrolled Keywords: | Differenciaegyenlet, Integrálegyenlet |
| Additional Information: | Bibliogr.: p. 23-24. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jan. 27. 14:02 |
| Last Modified: | 2021. Sep. 16. 10:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/66361 |
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