Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros
type: Item
instance of: scholarly article
title: Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros
author: Michael N. Vrahatis
published in: Topology and its Applications
publication date: 2020-04-07T00:00:00Z
review text: In this paper, two short proofs of a recently proposed intermediate value theorem for simplices are given in Theorem 2.1. The obtained proofs are based on Sperner covering principles, Lemmas 2.2 and 2.3. Theorem 3.1 deals with simplicial approximations of zeros of continuous mappings which is based on Theorem 2.1 and Sperner's Lemma 3.1. An error estimate is presented in Theorem 3.2. The technique used in Theorem 2.1 seems quite interesting.
reviewed by: Safeer Hussain Khan
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 91A44
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 7187683
zbMATH Keywords: Sperner covering
zbMATH Keywords: intermediate value theorems
zbMATH Keywords: Bolzano theorem
zbMATH Keywords: Bolzano-Poincaré-Miranda theorem
zbMATH Keywords: Brouwer fixed point theorem
zbMATH Keywords: Knaster-Kuratowski-Mazurkiewicz lemma
zbMATH Keywords: Sperner lemma
zbMATH Keywords: simplicial approximation
zbMATH Keywords: equilibria
zbMATH Keywords: mathematical economics
describes a project that uses: CHABIS
MaRDI profile type: Publication
full work available at URL: j.topol.2019.107036
OpenAlex ID: W2998674214
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Wikidata QID: Q126566684
DOI: 10.1016/J.TOPOL.2019.107036
description: scientific article; zbMATH DE number 7187683