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.2010 Mathematics Subject Classification. Primary 54H25; Secondary 47H09, 47H10.

No abstract