ON THE MODULAR SEQUENCE SPACES GENERATED BY THE CESÀRO MEAN

Sukhdev Singh     (Agam Tutorials, Adampur Doaba-144102, Jalandhar, Punjab, India; Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara-144411, Punjab, India)
Toseef Ahmed Malik     (Department of Mathematics, Govt. Boys Higher Secondary School, Darhal-185135, Jammu and Kashmir, India; Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara-144411, Punjab, India)

Abstract


In this paper, the seminormed Ces\`aro difference sequence space  \( \ell(\mathcal{F}_j, q, g, r, \mu, \Delta_{({s})}^{t}, \mathcal{C})\) is defined by using the  generalized Orlicz function. Some algebraic and topological properties of the space \(\ell(\mathcal{F}_j, q, g, r, \mu, \Delta_{({s})}^{t}, \mathcal{C}) \) are investigated. Various inclusion relations for this sequence space are also studied.

Keywords


Difference sequences, Orlicz function, Modular sequence, \(AK\)-space and \(BK\)-space

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References


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DOI: http://dx.doi.org/10.15826/umj.2024.2.013

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