Related papers: An elementary direct proof that the Knaster-Kurato…

We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…

These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We present a constructive proof of the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions. And we will show that the existence of such an equilibrium implies Sperner's lemma.…

This paper uses the Hartman-Stampacchia theorems as the primary tool to prove the Gale-Nikaid{\^o}-Debreu lemmas. It also establishes a cycle of equivalences among the Hartman-Stampacchia theorems, the Gale-Nikaid{\^o}-Debreu lemmas, and…

This paper first proves two fixed point theorems in complete random normed modules, which are respectively the random generalizations of the classical Banach's contraction mapping principle and Browder--Kirk's fixed point theorem. As…

We consider a generalization of the classic Sperner lemma. This lemma states that every Sperner coloring of a triangulation of a simplex contains a fully colored simplex. We found a weaker assumption than Sperner's coloring. It is also…

We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…

We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.

We prove a new fixed - point result for the image Im(j) of any continuous function j from K to (K x K), where K is a compact convex subset of a Hausdorff locally convex space, provided that the projection of Im(j) to the first factor is…

This paper shows, in the framework of the logical method,the unsolvability of $k$-set agreement task by devising a suitable formula of epistemic logic. The unsolvability of $k$-set agreement task is a well-known fact, which is a direct…

We prove a fixed point theorem that combines the contraction mapping principle and some Knaster-Tarski-like theorem. As a consequence we obtain an existence theorem to initial value problem for ordinary differential equation with…

We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of $n$-dimensional Euclidean space has a convergent subsequence…

In this paper, we introduce the notion of $\alpha$--contractive mapping of Meir--Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this…

Under the same assumptions made by Mas-Colell et al. (1995), I develop a short, simple, and complete proof of existence of equilibrium prices based on excess demand functions. The result is obtained by applying the Brouwer fixed point…

The Sperner and Tucker lemmas are combinatorial analogous of the Brouwer and Borsuk - Ulam theorems with many useful applications. These classic lemmas are concerning labellings of triangulated discs and spheres. In this paper we show that…

Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains…

By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…

We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…

We present a constructive proof of Brouwer's fixed point theorem with sequentially at most one fixed point, and apply it to the mini-max theorem of zero-sum games.