Viscosity iteration method in CAT(0) spaces without the nice projection property
© 2015, Kaewkhao et al. A complete CAT(0) space X is said to have the nice projection property (property N for short) if its metric projection onto a geodesic segment preserves points on each geodesic segment, that is, for any geodesic segment L in X and x,y∈X, m∈[x,y] implies (Formula presented.),...
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| Main Authors: | , , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84942100701&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/54626 |
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| Institution: | Chiang Mai University |
| Summary: | © 2015, Kaewkhao et al. A complete CAT(0) space X is said to have the nice projection property (property N for short) if its metric projection onto a geodesic segment preserves points on each geodesic segment, that is, for any geodesic segment L in X and x,y∈X, m∈[x,y] implies (Formula presented.), where P<inf>L</inf> denotes the metric projection from X onto L. In this paper, we prove a strong convergence theorem of a two-step viscosity iteration method for nonexpansive mappings in CAT(0) spaces without the condition on the property N. Our result gives an affirmative answer to a problem raised by Piatek (Numer. Funct. Anal. Optim. 34:1245-1264, 2013). |
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