c(0) Can be Renormed to Have the Fixed Point Property for Affine Nonexpansive Mappings
Yazarlar (2)
Prof. Dr. Veysel NEZİR Kafkas Üniversitesi, Türkiye
Prof. Dr. Nizami MUSTAFA Kafkas Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | FILOMAT (Q3) | ||
| Dergi ISSN | 0354-5180 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI | ||
| Makale Dili | İngilizce | Basım Tarihi | 12-2018 |
| Kabul Tarihi | – | Yayınlanma Tarihi | 01-01-2018 |
| Cilt / Sayı / Sayfa | 32 / 16 / 5645–5663 | DOI | 10.2298/FIL1816645N |
| Makale Linki | http://www.doiserbia.nb.rs/ft.aspx?id=0354-51801816645N | ||
| UAK Araştırma Alanları |
Matematiksel Analiz
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| Özet |
| P.K. Lin gave the first example of a non-reflexive Banach space (X,||?||) with the fixed point property (FPP) for nonexpansive mappings and showed this fact for (l1,||?||1) with the equivalent norm ||?|| given by ||x|| = sup k?N 8k/1+8k ?1,n=k |xn|, for all x = (xn)n?N ? l1. We wonder (c0, ||?||1) analogue of P.K. Lin?s work and we give positive answer if functions are affine nonexpansive. In our work, for x = (?k)k ? c0, we define |||x||| := lim p?? sup ?k?N ?k (?1,j=k |?j|p/2j)1/p where ?k ?k 3, k is strictly increasing with ?k > 2, ?k ? N, then we prove that (c0,|||?|||) has the fixed point property for affine |||?|||-nonexpansive self-mappings. Next, we generalize this result and show that if ?(?) is an equivalent norm to the usual norm on c0 such that lim sup n ?(1/n ?n,m=1 xm + x) = lim sup n ?(1/n ?n,m=1 xm) + ?(x) for every weakly null sequence (xn)n and for all x ? c0, then for every ? > 0, c0 with the norm ||?||? = ?(?)+?|||?||| has the FPP for affine ||?||?-nonexpansive self-mappings. |
| Anahtar Kelimeler |
BM Sürdürülebilir Kalkınma Amaçları
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