Interior fixed points of unit-sphere-preserving Euclidean maps

Interior fixed points of unit-sphere-preserving Euclidean maps

Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least one fixed point in the interior of the ball. We generalize Schirmer's result by provi...

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Main Authors: Nirattaya Khamsemanan, Robert F. Brown, Catherine Lee, Sompong Dhompongsa
Format: Journal
Published: 2018
Subjects:
Mathematics
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902592555&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/51820
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-518202018-09-04T06:09:40Z Interior fixed points of unit-sphere-preserving Euclidean maps Nirattaya Khamsemanan Robert F. Brown Catherine Lee Sompong Dhompongsa Mathematics Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least one fixed point in the interior of the ball. We generalize Schirmer's result by proving that a smooth self-map of Euclidean n-space that extends a self-map of the unit sphere of that class must have at least one fixed point in the interior of the unit ball. © 2012 Khamsemanan et al.; licensee Springer. 2018-09-04T06:09:40Z 2018-09-04T06:09:40Z 2012-01-01 Journal 16871812 16871820 2-s2.0-84902592555 10.1186/1687-1812-2012-183 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902592555&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/51820
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Nirattaya Khamsemanan
Robert F. Brown
Catherine Lee
Sompong Dhompongsa
Interior fixed points of unit-sphere-preserving Euclidean maps
description Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least one fixed point in the interior of the ball. We generalize Schirmer's result by proving that a smooth self-map of Euclidean n-space that extends a self-map of the unit sphere of that class must have at least one fixed point in the interior of the unit ball. © 2012 Khamsemanan et al.; licensee Springer.
format Journal
author Nirattaya Khamsemanan
Robert F. Brown
Catherine Lee
Sompong Dhompongsa
author_facet Nirattaya Khamsemanan
Robert F. Brown
Catherine Lee
Sompong Dhompongsa
author_sort Nirattaya Khamsemanan
title Interior fixed points of unit-sphere-preserving Euclidean maps
title_short Interior fixed points of unit-sphere-preserving Euclidean maps
title_full Interior fixed points of unit-sphere-preserving Euclidean maps
title_fullStr Interior fixed points of unit-sphere-preserving Euclidean maps
title_full_unstemmed Interior fixed points of unit-sphere-preserving Euclidean maps
title_sort interior fixed points of unit-sphere-preserving euclidean maps
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902592555&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/51820
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