Mathematical Logic Quarterly 63 (5):454-461 (2017)

Abstract
In this paper, we investigate the logical strength of two types of fixed point theorems in the context of reverse mathematics. One is concerned with extensions of the Banach contraction principle. Among theorems in this type, we mainly show that the Caristi fixed point theorem is equivalent to math formula over math formula. The other is dedicated to topological fixed point theorems such as the Brouwer fixed point theorem. We introduce some variants of the Fan-Browder fixed point theorem and the Kakutani fixed point theorem, which we call math formula and math formula, respectively. Then we show that math formula is equivalent to math formula and math formula is equivalent to math formula, over math formula. In addition, we also study the application of the Fan-Browder fixed point theorem to game systems.
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DOI 10.1002/malq.201600096
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References found in this work BETA

Located Sets and Reverse Mathematics.Mariagnese Giusto & Stephen G. Simpson - 2000 - Journal of Symbolic Logic 65 (3):1451-1480.
Fixed Point Theory in Weak Second-Order Arithmetic.Naoki Shioji & Kazuyuki Tanaka - 1990 - Annals of Pure and Applied Logic 47 (2):167-188.
Reverse Mathematics and Order Theoretic Fixed Point Theorems.Takashi Sato & Takeshi Yamazaki - 2017 - Archive for Mathematical Logic 56 (3-4):385-396.

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