A Proof Pearl with the Fan Theorem and Bar Induction

2011 ◽  
pp. 353-368 ◽  
Author(s):  
Keiko Nakata ◽  
Tarmo Uustalu ◽  
Marc Bezem
Keyword(s):  
Fan Theorem

scholarly journals SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

2014 ◽  
Vol 79 (3) ◽  
pp. 792-813 ◽  
Author(s):  
ROBERT S. LUBARSKY ◽  
HANNES DIENER
Keyword(s):  
Constructive Mathematics ◽  
Kripke Models ◽  
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.

scholarly journals Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

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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