Paper Info
Title
Two kinds of fixed point theorems and reverse mathematics.
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 ACA over RCA(0). 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 FBFP and KFP, respectively. Then we show that FBFP is equivalent to WKL and KFP is equivalent to ACA, over RCA(0). In addition, we also study the application of the Fan-Browder fixed point theorem to game systems. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Year
DOI
Venue
2017
10.1002/malq.201600096
MATHEMATICAL LOGIC QUARTERLY
Field
DocType
Volume
Discrete mathematics,Reverse mathematics,Fixed-point theorem,Mathematics
Journal
63
Issue
ISSN
Citations 
5
0942-5616
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Weiguang Peng100.34
Takeshi Yamazaki232.15