Abundance of equivalent norms on c(0) with fixed point property for affine nonexpansive mappings
Yazarlar (2)
Prof. Dr. Veysel NEZİR Kafkas Üniversitesi, Türkiye
Sıddık Sade
Kafkas Üniversitesi, Türkiye
Kafkas Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(ESCI dergilerinde yayınlanan tam makale)
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| Dergi Adı | Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics | ||
| Dergi ISSN | 1303-5991 Wos Dergi | ||
| Dergi Tarandığı Indeksler | ESCI | ||
| Makale Dili | İngilizce | Basım Tarihi | 06-2018 |
| Cilt / Sayı / Sayfa | 67 / 1 / 1–28 | DOI | 10.1501/Commual_0000000826 |
| Makale Linki | http://dergiler.ankara.edu.tr/dergiler/29/2198/22814.pdf | ||
| Özet |
| In 1979, K. Goebel and T. Kuczumow showed that a large classof closed, bounded, convex (c.b.c.), non-weak*-compact subsets K of $ l1$ hasthe fixed point property for nonexpansive mappings. Later, in 2008, P.K. Linproved that $ l1$ can be renormed to have the fixed point property for nonex-pansive mappings. Then, Nezir recently worked on $ c0$ -analogue of Goebel andKuczumow's theorem with an equivalent norm and showed that there existsa large class of equivalent norms$ k k$ on $ c0$ for which there exist non-weaklycompact closed, bounded, convex subsets that have the fixed point propertyfor affine $ k k$ -nonexpansive mappings. In fact, he sees that his examples areclosed, convex hulls of some asymptotically isometric (ai) $ c0$ -summing basicsequences whereas Lennard and Nezir in 2011 showed that the closed, convexhull of any ai $ c0$ -summing basic sequence fails the xed point property foraffine $ k k1$ -nonexpansive mappings. In this work, we show that equivalentnorms with fixed point property for affine nonexpansive mappings are some-what abundant. Firstly, we construct many types of equivalent norms andeven show some norms are exactly the same as the natural norm while it isnot clear to see that in the beginning, and then we show with our new type ofequivalent norms $c0$ do not contain any asymptotically isometric copy of $ c0$ .Next, we see that Nezir's equivalent norms are not the only ones with fixedpoint property for affine nonexpansive mappings on his sets. |
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BM Sürdürülebilir Kalkınma Amaçları
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