On some generalized $ q $-difference sequence spaces

Hacer Bilgin Ellidokuzoğlu; Serkan Demiriz; Hacer Bilgin Ellidokuzoğlu; Serkan Demiriz

doi:10.3934/math.2023947

AIMS Mathematics

2023, Volume 8, Issue 8: 18607-18617. doi: 10.3934/math.2023947

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Research article

On some generalized $ q $-difference sequence spaces

Hacer Bilgin Ellidokuzoğlu ¹,
Serkan Demiriz ^{2
,
,}

1.
Department of Mathematics, Recep Tayyip Erdo$\tilde{{\rm{g}}}$an University, Rize 53100, Turkey
2.
Department of Mathematics, Tokat Gaziosmanpaşa University, Tokat 60240, Turkey

Received: 17 March 2023 Revised: 18 May 2023 Accepted: 28 May 2023 Published: 01 June 2023
MSC : 40C05, 40G05, 33D99

In this study, we construct the spaces of $ q $-difference sequences of order $ m $. We obtain some inclusion relations, topological properties, Schauder basis and alpha, beta and gamma duals of the newly defined spaces. We characterize certain matrix classes from the newly defined spaces to any one of the spaces $ c_0, c, \ell_\infty $ and $ \ell_p $.
- sequence spaces,
- $ q $-calculus,
- $ q $-difference matrix,
- $ q $-difference sequence spaces
Citation: Hacer Bilgin Ellidokuzoğlu, Serkan Demiriz. On some generalized $ q $-difference sequence spaces[J]. AIMS Mathematics, 2023, 8(8): 18607-18617. doi: 10.3934/math.2023947

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Abstract

In this study, we construct the spaces of $ q $-difference sequences of order $ m $. We obtain some inclusion relations, topological properties, Schauder basis and alpha, beta and gamma duals of the newly defined spaces. We characterize certain matrix classes from the newly defined spaces to any one of the spaces $ c_0, c, \ell_\infty $ and $ \ell_p $.

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