Fixed point properties for a degenerate Lorentz-Marcinkiewicz space
Yazarlar (1)
Prof. Dr. Veysel NEZİR
Kafkas Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Turkish Journal of Mathematics (Q3) | ||
| Dergi ISSN | 1300-0098 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI | ||
| Makale Dili | İngilizce | Basım Tarihi | 07-2019 |
| Cilt / Sayı / Sayfa | 43 / 4 / 1919–1939 | DOI | 10.3906/mat-1802-79 |
| Özet |
| We construct an equivalent renorming of ℓ1 , which turns out to produce a degenerate ℓ1 -analog Lorentz–Marcinkiewicz space ℓ;1 , where the weight sequence = (n)n2N = (2; 1; 1; 1;) is a decreasing positive sequence inℓ1nc0 , rather than in c0nℓ1 (the usual Lorentz situation). Then we obtain its isometrically isomorphic predual ℓ0;1 anddual ℓ;1, corresponding degenerate c0 -analog and ℓ1-analog Lorentz–Marcinkiewicz spaces, respectively. We provethat both spaces ℓ;1 and ℓ0;1 enjoy the weak fixed point property (w-fpp) for nonexpansive mappings yet they failto have the fixed point property (fpp) for nonexpansive mappings since they contain an asymptotically isometric copyof ℓ1 and c0 , respectively. In fact, we prove for both spaces that there exist nonempty, closed, bounded, and convexsubsets with invariant fixed point-free affine, nonexpansive mappings on them and so they fail to have fpp for affinenonexpansive mappings. Also, we show that any nonreflexive subspace of l0;1 contains an isomorphic copy of c0 and sofails fpp for strongly asymptotically nonexpansive maps. Finally, we get a Goebel and Kuczumow analogy by provingthat there exists an infinite dimensional subspace of ℓ;1 with fpp for affine nonexpansive mappings. |
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BM Sürdürülebilir Kalkınma Amaçları
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| TRDizin | 2 |