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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2022 / Cilt: 6 - Sayı: 3

Some new equivalents of the Brouwer fixed point theorem

Sehie PARK
Pages
300–309
Publication Date
2022-09-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Consequently, we add up our large list of such equivalents.

📌 3 Key Takeaways

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Objective & Hypothesis:This is to recollect the equivalent formulations of the Brouwer fixed point theorem.
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Key Findings & Data:We collect a large number of recently known sources of such equivalents.
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Conclusion & Impact:Consequently, we add up our large list of such equivalents.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Abstract convex space · KKM theorem · KKM class of multimaps

Abstract

This is to recollect the equivalent formulations of the Brouwer fixed point theorem. We collect a large number of recently known sources of such equivalents. More recently, Jinlu Li obtained two fixed point theorems on newly defined quasi-point-separable topological vector spaces. His theorems extend the Tychonoff fixed point theorem on locally convex t.v.s. However, we note that his new theorems are logically equivalent to the Brouwer fixed point theorem. Consequently, we add up our large list of such equivalents.

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Cite This Article

PARK, S. (2022). Some new equivalents of the Brouwer fixed point theorem. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 6 - Sayı: 3, 300–309. https://ajindex.com/articles/729014

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