On the $q$-Cesaro bounded double sequence space

Year 2024, Volume: 12 Issue: 3, 145 - 154

Sezer Erdem

https://doi.org/10.36753/mathenot.1492238

Abstract

In this article, the new sequence space $\tilde{\mathcal{M}}_u^q$ is acquainted, described as the domain of the 4d (4-dimensional) $q$-Cesaro matrix operator, which is the $q$-analogue of the first order 4d Cesaro matrix operator, on the space of bounded double sequences. In the continuation of the study, the completeness of the new space is given, and the inclusion relation related to the space is presented. In the last two parts, the duals of the space are determined, and some matrix classes are acquired.

Keywords

$q$-analogue, 4d $q$-Cesaro matrix, Double sequence space, Duals, Matrix transformations

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