Caristi-Kirk and Oettli-Th��ra Ball Spaces and applications
| Autor: | B��aszkiewicz, Piotr, ��miel, Hanna, Linzi, Alessandro, Szewczyk, Piotr |
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| Rok vydání: | 2019 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1901.03853 |
| Popis: | Based on the theory of ball spaces introduced by Kuhlmann and Kuhlmann we introduce and study Caristi-Kirk and Oettli-Th��ra ball spaces. We show that if the underlying metric space is complete, then these have a very strong property: every ball contains a singleton ball. This fact provides quick proofs for several results which are equivalent to the Caristi-Kirk Fixed Point Theorem, namely Ekeland's Variational Principles, the Oettli-Th��ra Theorem, Takahashi's Theorem and the Flower Petal Theorem. 15 pages, submitted to Journal of Fixed Point Theory and Applications |
| Databáze: | OpenAIRE |
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