A decomposition of Brouwer’s fan theorem

AbstractVarieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

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A new short proof of Fan Theorem

Journal of Discrete Mathematical Sciences and Cryptography ◽

10.1080/09720529.2013.802406 ◽

2013 ◽

Vol 16 (2-03) ◽

pp. 163-165

Author(s):

Kewen Zhao

Keyword(s):

Short Proof ◽

Fan Theorem

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König's lemma, weak König's lemma, and the decidable fan theorem

Mathematical Logic Quarterly ◽

10.1002/malq.202000020 ◽

2021 ◽

Author(s):

Makoto Fujiwara

Keyword(s):

Fan Theorem ◽

Weak König’S Lemma ◽

König’S Lemma

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Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

Abstract and Applied Analysis ◽

10.1155/2014/497846 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6

Author(s):

Adem Kılıçman ◽

Rais Ahmad ◽

Mijanur Rahaman

Keyword(s):

Equilibrium Problem ◽

Existence Results ◽

Vector Equilibrium Problem ◽

Vector Spaces ◽

Multivalued Mappings ◽

Topological Vector Spaces ◽

Fan Theorem ◽

Special Cases ◽

Vector Equilibrium ◽

Generalized Pseudomonotonicity

We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.

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