Geodesic
A study on q-analogue of Catalan sequence spaces
Filomat, Tome 37 (2023) no. 3, p. 839

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DOI

In this study, we construct q-analog C(q) of Catalan matrix and study the sequence spaces c 0 (C(q)) and c(C(q)) defined as the domain of q-Catalan matrix C(q) in the spaces c 0 and c, respectively. We exhibit some topological properties, obtain Schauder bases and determine α-, β-, and γ-duals of the spaces c 0 (C(q)) and c(C(q)). Finally, we characterize certain class of matrix mappings from the spaces c 0 (C(q)) and c(C(q)) to the space µ = {ℓ ∞ , c 0 , c, ℓ 1 } and give the necessary and sufficient conditions for a matrix operator to be compact.
DOI : 10.2298/FIL2303839Y
Classification : 46A45, 46B45, 47B07
Keywords: Sequence space, q-Catalan matrix, Schauder basis, α-, β-, γ-duals, Matrix mappings, Compact operator, Hausdorff measure of non-compactness 
Taja Yaying; Merve Ìlkhan Kara; Bipan Hazarika; Emran Evren Kara. A study on q-analogue of Catalan sequence spaces. Filomat, Tome 37 (2023) no. 3, p. 839 . doi: 10.2298/FIL2303839Y
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     author = {Taja Yaying and Merve \`Ilkhan Kara and Bipan Hazarika and Emran Evren Kara},
     title = {A study on q-analogue of {Catalan} sequence spaces},
     journal = {Filomat},
     pages = {839 },
     year = {2023},
     volume = {37},
     number = {3},
     doi = {10.2298/FIL2303839Y},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2303839Y/}
}
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