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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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2020
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| Subjects: | |
| Online Access: | 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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| Institution: | Chiang Mai University |
| Summary: | © 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. |
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