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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th-cmuir.6653943832-546262018-09-04T10:19:01Z Viscosity iteration method in CAT(0) spaces without the nice projection property Attapol Kaewkhao Bancha Panyanak Suthep Suantai Mathematics © 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). 2018-09-04T10:19:01Z 2018-09-04T10:19:01Z 2015-12-25 Journal 1029242X 10255834 2-s2.0-84942100701 10.1186/s13660-015-0801-6 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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Mathematics Attapol Kaewkhao Bancha Panyanak Suthep Suantai Viscosity iteration method in CAT(0) spaces without the nice projection property |
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© 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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Journal |
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Attapol Kaewkhao Bancha Panyanak Suthep Suantai |
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Attapol Kaewkhao Bancha Panyanak Suthep Suantai |
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Attapol Kaewkhao |
| title |
Viscosity iteration method in CAT(0) spaces without the nice projection property |
| title_short |
Viscosity iteration method in CAT(0) spaces without the nice projection property |
| title_full |
Viscosity iteration method in CAT(0) spaces without the nice projection property |
| title_fullStr |
Viscosity iteration method in CAT(0) spaces without the nice projection property |
| title_full_unstemmed |
Viscosity iteration method in CAT(0) spaces without the nice projection property |
| title_sort |
viscosity iteration method in cat(0) spaces without the nice projection property |
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2018 |
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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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