Constructive proofs of Tychonoff's and Schauder's fixed point theorems
  for sequentially locally non-constant functions

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Abstract

We present a constructive proof of Tychonoff's fixed point theorem in a locally convex space for sequentially locally non-constant functions, As a corollary to this theorem we also present Schauder's fixed point theorem in a Banach space for sequentially locally non-constant functions. We follow the Bishop style constructive mathematics.

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Rental Harmony: Sperner's Lemma in Fair Division

Francis Edward Su (1999)

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The fan theorem and unique existence of maxima

Josef Berger, Douglas Bridges, Peter Schuster (2006)

The existence and uniqueness of a maximum point for a continuous real–valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.