Geodesic
The generalised double Hahn sequence space $H_\vartheta^{d}$
Medine Yeşilkayagil Savaşcı1 ; Feyzi Başar2 ; Medine Yeşilkayagil Savaşcı ; Feyzi Başar
1Faculty of Applied Sciences, Uşak University, Uşak, Türkiye
2Department of Primary Mathematics Teacher Education, İnönü University, Malatya, Türkiye
Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 2, pp. 101-114 
Medine Yeşilkayagil Savaşcı; Feyzi Başar; Medine Yeşilkayagil Savaşcı; Feyzi Başar. The generalised double Hahn sequence space $H_\vartheta^{d}$. Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 2, pp. 101-114. http://geodesic.mathdoc.fr/item/AMUC_2024_93_2_a2/
@article{AMUC_2024_93_2_a2,
     author = {Medine Ye\c{s}ilkayagil Sava\c{s}c{\i} and Feyzi Ba\c{s}ar and Medine Ye\c{s}ilkayagil Sava\c{s}c{\i} and Feyzi Ba\c{s}ar},
     title = { The generalised double {Hahn} sequence space $H_\vartheta^{d}$},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {101--114},
     year = {2024},
     volume = {93},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2024_93_2_a2/}
}
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Voir la notice de l'article provenant de la source Comenius University

Suppose that $\vartheta\in\{bp,r\}$. In this study, we introduce the generalised double Hahn sequence space $ H_\vartheta^{d} $ as an extension of generalised Hahn sequence space $h_d$ defined by Goes [J. Math. Anal. Appl. \textbf{39} (1972), 477--494]. We give some topological properties of this space. Then, we characterize the classes $ (H_\vartheta^{d} : W) $ of four dimensional infinite matrices, where $ W \in \{\mathcal{C_\vartheta, \mathcal{M}_u, \mathcal{L}_u, H_\vartheta^{d}\} $. Finally, we determine the $ \alpha $-dual of the space $ H_\vartheta^{d} $ and $ \beta(bp) $- and $ \gamma$-duals of the space H_r^{d} $.