SOME NEW SEQUENCE SPACES WHICH INCLUDE THE SPACES lP AND l∞
By Cafer Aydm, Feyzi Basar. 2005
81 citations recorded by the source corpus.
In the present paper, we introduce the sequence space a£ of non-absolute type and prove that the spaces arv and l v are linearly isomorphic for 0 < ρ < oo. We also show that dp, which includes the space l p , is a p-normed space and a Β Κ space in the cases of 0 < ρ < 1 and 1 < ρ < oo, respectively. Furthermore, we give some inclusion relations and determine the α-, βand 7-duals of the space a£ and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space aTv to some of the known sequence spaces and to some new sequence spaces.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d2af4c9e7e1c71bb0348854dca510186737e0775
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In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- ON THE SPACES OF LAMDA−CONVERGENT AND BOUNDED SEQUENCES (2010, methodology): “The approach constructing a new sequence space by means of the matrix domain of a particular limitation method has recently been employed by several authors, see for instance [1, 2, 3, 4, 8, 10, 12, 13] and [14].”
- ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX (2014, methodology): “In recent years, constructing a new sequence space by means of the domain of an infinite matrix was used by Wang [46], Ng and Lee [38], Malkowsky [32], Altay and Başar [2–5], Malkowsky and Savaş [35], Başar, Malkowsky and Altay [17], Başarır [19], Aydın and Başar [6–9], Başar, Altay and Mursaleen [1”
- On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I (2011, background): “The main purpose of the present paper, following [1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 16, 18] and [19], is to introduce the sequence spaces `p and ` λ ∞ of non-absolute type and is to derive some results related to them.”