On the modular sequence spaces generated by the Cesàro mean
Ural mathematical journal, Tome 10 (2024) no. 2, pp. 144-156 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, the seminormed Cesàro 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
@article{UMJ_2024_10_2_a12,
     author = {Sukhde Singh and Toseef Ahmed Malik},
     title = {On the modular sequence spaces generated by the {Ces\`aro} mean},
     journal = {Ural mathematical journal},
     pages = {144--156},
     year = {2024},
     volume = {10},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2024_10_2_a12/}
}
TY  - JOUR
AU  - Sukhde Singh
AU  - Toseef Ahmed Malik
TI  - On the modular sequence spaces generated by the Cesàro mean
JO  - Ural mathematical journal
PY  - 2024
SP  - 144
EP  - 156
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2024_10_2_a12/
LA  - en
ID  - UMJ_2024_10_2_a12
ER  - 
%0 Journal Article
%A Sukhde Singh
%A Toseef Ahmed Malik
%T On the modular sequence spaces generated by the Cesàro mean
%J Ural mathematical journal
%D 2024
%P 144-156
%V 10
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2024_10_2_a12/
%G en
%F UMJ_2024_10_2_a12
Sukhde Singh; Toseef Ahmed Malik. On the modular sequence spaces generated by the Cesàro mean. Ural mathematical journal, Tome 10 (2024) no. 2, pp. 144-156. http://geodesic.mathdoc.fr/item/UMJ_2024_10_2_a12/

[1] Altay B., Başar F., “Generalization of the sequence space $\ell(p)$ derived by weighted means”, J. of Math. Anal. Appl., 330:1 (2007), 174–185 | DOI | MR | Zbl

[2] Bakery A. A., Kalthum Om, Mohamed S. K., “Orlicz generalized difference sequence space and the linked pre-quasi operator ideal”, J. of Math., 2020, 6664996, 1–9 | DOI | MR

[3] Dutta H., Basar F., “A generalization of Orlicz sequence spaces by Cesàro mean of order one”, Acta Math. Univ. Comenian, 80:2 (2011), 185–200 | MR | Zbl

[4] Esi A., Bipin H., Esi A., “New type of lacunary Orlicz difference sequence spaces generated by infinite matrices”, Filomat, 30:12 (2016), 3195–3208 | DOI | MR | Zbl

[5] Et M., Çolak R., “On some generalized sequence spaces”, Soochow J. Math., 21:4 (1995), 377–386 | MR

[6] Et M., Lee P. Y., Tripathy B. C., “Strongly almost $(V, \lambda)(\Lambda^r)$-summable sequences defined by Orlicz function”, Hokkaido Math. J., 35 (2006), 197–213 | MR | Zbl

[7] Gupta M., Bhar A., “Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals”, Math. Slovaca, 64:6 (2014), 1474–1496 | DOI | MR

[8] Jebril I. H., “A generalization of strongly Cesàro and strongly lacunary summable spaces”, Acta Univ. Apalensis, 23 (2010), 49–61 | MR | Zbl

[9] Kizmaz H., “On certain sequence spaces”, Canad. Math. Bull., 24:2 (1981), 169–176 | DOI | MR | Zbl

[10] Lindenstrauss J., Tzafriri L., “On Orlicz sequence spaces”, Israel J. Math., 10 (1971), 379–390 | DOI | MR | Zbl

[11] Mursaleen M., Khan A. M., Qamaruddin, “Difference sequence spaces defined by Orlicz functions”, Demonstratio Math., 32:1 (1999), 145–150 | DOI | MR | Zbl

[12] Nakano H., “Modulared sequence spaces”, Proc. Japan Acad., 27:9 (1951), 508–512 | DOI | MR | Zbl

[13] Orlicz W., “Über Räume $(L^M)$”, Bull. Int. Acad. Polon. Sci., 1936, 93–107 (in German) | Zbl

[14] Tripathy B. C., Esi A., “A new type of difference sequence spaces”, Inter. J. Sci. Tech., 1:1 (2006), 11–14

[15] Tripathy B. C., Choudhary B., Sarma B., “Some difference double sequence spaces defined by Orlicz function”, Kyungpook Math. J., 48:4 (2008), 613–622 | DOI | MR | Zbl

[16] Tripathy B. C., Dutta H., “Some difference paranormed sequence spaces defined by Orlicz functions”, Fasc. Math., 42 (2009), 121–131 | MR | Zbl

[17] Tripathy B. C., Dutta H., “On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and $q$-lacunary $\Delta^n_m$-statistical convergence”, An. Ştiint. Univ. Ovidius Constanţa. Ser. Mat., 20:1 (2012), 417–430 | MR | Zbl

[18] Woo J., “On modular sequence spaces”, Studia Math., 48:3 (1973), 271–289 | DOI | MR | Zbl