Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup>
© 2019 by the Mathematical Association of Thailand. Let X be a surface in R3. A subset E of X is said to be convex if, for each p, q ∈ E, it contains each shortest geodesic joining p and q. A surface in R3 is said to have the fixed point property if each continuous mapping T: E → E from a compact co...
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th-cmuir.6653943832-678902020-04-02T15:10:27Z Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> Preeyaporn Thongin Worapong Fupinwong Mathematics © 2019 by the Mathematical Association of Thailand. Let X be a surface in R3. A subset E of X is said to be convex if, for each p, q ∈ E, it contains each shortest geodesic joining p and q. A surface in R3 is said to have the fixed point property if each continuous mapping T: E → E from a compact convex subset E of X has a fixed point. In this paper, we give some examples of surfaces in R3 that do not have the fixed point property. Moreover, we show that the surface z = y2 and the upper hemisphere of the sphere of radius r centered at (0, 0, 0) with north pole and equator removed have the fixed point property. 2020-04-02T15:10:27Z 2020-04-02T15:10:27Z 2019-12-01 Journal 16860209 2-s2.0-85077550522 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85077550522&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67890 |
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Mathematics Preeyaporn Thongin Worapong Fupinwong Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> |
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© 2019 by the Mathematical Association of Thailand. Let X be a surface in R3. A subset E of X is said to be convex if, for each p, q ∈ E, it contains each shortest geodesic joining p and q. A surface in R3 is said to have the fixed point property if each continuous mapping T: E → E from a compact convex subset E of X has a fixed point. In this paper, we give some examples of surfaces in R3 that do not have the fixed point property. Moreover, we show that the surface z = y2 and the upper hemisphere of the sphere of radius r centered at (0, 0, 0) with north pole and equator removed have the fixed point property. |
| format |
Journal |
| author |
Preeyaporn Thongin Worapong Fupinwong |
| author_facet |
Preeyaporn Thongin Worapong Fupinwong |
| author_sort |
Preeyaporn Thongin |
| title |
Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> |
| title_short |
Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> |
| title_full |
Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> |
| title_fullStr |
Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> |
| title_full_unstemmed |
Remarks on brouwer fixed point theorem for some surfaces in R<sup>3</sup> |
| title_sort |
remarks on brouwer fixed point theorem for some surfaces in r<sup>3</sup> |
| publishDate |
2020 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85077550522&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67890 |
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