Caristi–Kirk and Oettli–Théra ball spaces and applications

Autor:	Piotr Błaszkiewicz, Alessandro Linzi, Hanna Ćmiel, Piotr Szewczyk
Rok vydání:	2019
Předmět:	Discrete mathematics Metric space Singleton Applied Mathematics Modeling and Simulation Fixed-point theorem Geometry and Topology Ball (mathematics) Mathematical proof Mathematics
Zdroj:	Journal of Fixed Point Theory and Applications. 21
ISSN:	1661-7746 1661-7738
DOI:	10.1007/s11784-019-0729-4
Popis:	Based on the theory of ball spaces introduced by Kuhlmann and Kuhlmann, we introduce and study Caristi–Kirk and Oettli–Théra 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–Théra theorem, Takahashi’s theorem and the flower petal theorem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::60dc8c52e605a084f9efd966deed3492 https://doi.org/10.1007/s11784-019-0729-4 Zobrazit plný text záznamu Full text from SpringerLink