Geodesic
A large class in Köthe-Toeplitz duals of generalized Cesàro difference sequence spaces with fixed point property for nonexpansive mappings
Filomat, Tome 36 (2022) no. 17, p. 5795

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DOI

In 1970, Cesàro sequence spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ℓ ∞ , c 0 and c. Then, in 1983, Orhan introduced Cesàro difference sequence spaces. Both works used difference operator and investigated Köthe-Toeplitz duals for the new Banach spaces they introduced. Later, various authors generalized these new spaces, especially the one introduced by Orhan. In this study, first we discuss the fixed point property for these spaces. Then, we recall that Goebel and Kuczumow showed that there exists a very large class of closed, bounded, convex subsets in Banach space of absolutely summable scalar sequences, ℓ 1 with fixed point property for nonexpansive mappings. So we consider a Goebel and Kuczumow analogue result for a Köthe-Toeplitz dual of a generalized Cesàro difference sequence space. We show that there exists a large class of closed, bounded and convex subsets of these spaces with fixed point property for nonexpansive mappings.
DOI : 10.2298/FIL2217795N
Classification : 46B45, 47H09, 46B10
Keywords: Nonexpansive mapping, fixed point property, renorming, closed bounded convex set, Cesàro difference sequences, Köthe-Toeplitz dual 
Veysel Nezir; Hemen Dutta; Selçuk Yıldırım. A large class in Köthe-Toeplitz duals of generalized Cesàro difference sequence spaces with fixed point property for nonexpansive mappings. Filomat, Tome 36 (2022) no. 17, p. 5795 . doi: 10.2298/FIL2217795N
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     title = {A large class in {K\"othe-Toeplitz} duals of generalized {Ces\`aro} difference sequence spaces with fixed point property for nonexpansive mappings},
     journal = {Filomat},
     pages = {5795 },
     year = {2022},
     volume = {36},
     number = {17},
     doi = {10.2298/FIL2217795N},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2217795N/}
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