We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Constructive Proof of Brouwer's Fixed Point Theorem for Sequentially Locally Non-constant and Uniformly Sequentially Continuous Functions.
- Authors
Tanaka, Yasuhito
- Abstract
We present a constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions based on the existence of approximate fixed points. And we will show that our Brouwer's fixed point theorem implies Sperner's lemma for a simplex. Since the existence of approximate fixed points is derived from Sperner's lemma, our Brouwer's fixed point theorem is equivalent to Sperner's lemma.
- Subjects
PROOF theory; FIXED point theory; MATHEMATICAL sequences; CONTINUOUS functions; MATHEMATICAL constants; EXISTENCE theorems; APPROXIMATION theory
- Publication
IAENG International Journal of Applied Mathematics, 2012, Vol 42, Issue 1, p1
- ISSN
1992-9978
- Publication type
Article