FIXED POINT THEOREM IN BALL SPACES AND CARISTI'S FIXED POINT THEOREM

The purpose of this paper is to introduce a fixed point theorem in a ball space, which is proved without the Axiom of Choice. Moreover, using the fixed point theorem in a ball space, we prove Caristi's fixed point theorem. Therefore the proof of Caristi's fixed point theorem in this paper does not depend on the Axiom of Choice.