Fixed point property of direct sums
For a uniformly convex space Z, we show that Z-direct sums (X1⊕⋯⊕XN)Z of Banach spaces X1,...,XN with R(a,Xi)<1+a for some a ∈(0,1] have the fixed point property for nonexpansive mappings. As a direct consequence, the result holds for all ψ-direct sums with ψ being strictly convex. The same resul...
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th-cmuir.6653943832-622892018-09-11T09:25:11Z Fixed point property of direct sums S. Dhompongsa A. Kaewcharoen A. Kaewkhao Mathematics For a uniformly convex space Z, we show that Z-direct sums (X1⊕⋯⊕XN)Z of Banach spaces X1,...,XN with R(a,Xi)<1+a for some a ∈(0,1] have the fixed point property for nonexpansive mappings. As a direct consequence, the result holds for all ψ-direct sums with ψ being strictly convex. The same result is extended to all ψ-direct sums X⊕ψY of spaces X and Y with property (M), whenever ψ≠ψ1. The permanence of properties that are sufficient for the fixed point property are obtained for Z-direct sums (and then for ψ-direct sums). Such properties include the properties R(X)<2, WNUS, CNJ(a,X)<2, UKK, and NUC. © 2005 Elsevier Ltd. All rights reserved. 2018-09-11T09:25:11Z 2018-09-11T09:25:11Z 2005-11-30 Journal 0362546X 2-s2.0-28044438707 10.1016/j.na.2005.02.020 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=28044438707&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62289 |
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Mathematics |
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Mathematics S. Dhompongsa A. Kaewcharoen A. Kaewkhao Fixed point property of direct sums |
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For a uniformly convex space Z, we show that Z-direct sums (X1⊕⋯⊕XN)Z of Banach spaces X1,...,XN with R(a,Xi)<1+a for some a ∈(0,1] have the fixed point property for nonexpansive mappings. As a direct consequence, the result holds for all ψ-direct sums with ψ being strictly convex. The same result is extended to all ψ-direct sums X⊕ψY of spaces X and Y with property (M), whenever ψ≠ψ1. The permanence of properties that are sufficient for the fixed point property are obtained for Z-direct sums (and then for ψ-direct sums). Such properties include the properties R(X)<2, WNUS, CNJ(a,X)<2, UKK, and NUC. © 2005 Elsevier Ltd. All rights reserved. |
| format |
Journal |
| author |
S. Dhompongsa A. Kaewcharoen A. Kaewkhao |
| author_facet |
S. Dhompongsa A. Kaewcharoen A. Kaewkhao |
| author_sort |
S. Dhompongsa |
| title |
Fixed point property of direct sums |
| title_short |
Fixed point property of direct sums |
| title_full |
Fixed point property of direct sums |
| title_fullStr |
Fixed point property of direct sums |
| title_full_unstemmed |
Fixed point property of direct sums |
| title_sort |
fixed point property of direct sums |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=28044438707&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62289 |
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