<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This study includes the new Banach space <inline-formula id="j_aupcsm-2023-0009_eq_002"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_aupcsm-2023-0009_eq_002.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="M2"><msubsup><mover accent="true"><mi>ℒ</mi><mo>˜</mo></mover><mi>s</mi><mi>q</mi></msubsup></math><tex-math>$$\tilde {\cal L}_s^q$$</tex-math></alternatives></inline-formula> designed as the domain in 𝓛<sub><italic>s</italic></sub> space of the 4d (4-dimensional) <italic>q</italic>-Cesàro matrix obtained as the <italic>q</italic>-analog of the well-known 4d Cesàro matrix. After showing the completeness of the aforementioned space, giving some inclusion relations, determining the fundamental set of this space and calculating the duals, finally, some matrix transformations related to the new space were characterized.</p>
</abstract>

This study includes the new Banach space ℒ˜sq$$\tilde {\cal L}_s^q$$ designed as the domain in 𝓛s space of the 4d (4-dimensional) q-Cesàro matrix obtained as the q-analog of the well-known 4d Cesàro matrix. After showing the completeness of the aforementioned space, giving some inclusion relations, determining the fundamental set of this space and calculating the duals, finally, some matrix transformations related to the new space were characterized.

<italic>q</italic>-Cesàro double sequence space <inline-formula id="j_aupcsm-2023-0009_eq_001"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_aupcsm-2023-0009_eq_001.png"/><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="M1"><msubsup><mover accent="true"><mi>ℒ</mi><mo>˜</mo></mover><mi>s</mi><mi>q</mi></msubsup></math><tex-math>$$\tilde {\cal L}_s^q$$</tex-math></alternatives></inline-formula> derived by <italic>q</italic>-analog

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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-Cesàro double sequence space  derived by -analog

This study includes the new Banach space ℒ˜sq$$\tilde {\cal L}_s^q$$ designed as the domain in 𝓛s space of the 4d (4-dimensional) q-Cesàro matrix obtained as...

q-Cesàro double sequence space ${\tilde{ℒ}}_{s}^{q}$ $$\tilde {\cal L}_s^q$$ derived by q-analog

Published Online: Jul 31, 2023

Page range: 111 - 126

Received: Feb 10, 2023

Accepted: May 09, 2023

DOI: https://doi.org/10.2478/aupcsm-2023-0009

© 2023 Sezer Erdem et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

q-Cesàro double sequence space ℒ˜sq$$\tilde {\cal L}_s^q$$ derived by q-analog

Published Online: Jul 31, 2023

Page range: 111 - 126

Received: Feb 10, 2023

Accepted: May 09, 2023

DOI: https://doi.org/10.2478/aupcsm-2023-0009

© 2023 Sezer Erdem et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

q-Cesàro double sequence space ${\tilde{ℒ}}_{s}^{q}$ $$\tilde {\cal L}_s^q$$ derived by q-analog