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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  ℓ(Fj,q,g,r,μ,Δt(s),C) is defined by using the  generalized Orlicz function. Some algebraic and topological properties of the space ℓ(Fj,q,g,r,μ,Δt(s),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


  1. Altay B., Başar F. Generalization of the sequence space ℓ(p) derived by weighted means. J. of Math. Anal. Appl., 2007. Vol. 330, No. 1. P. 174–185. DOI: 10.1016/j.jmaa.2006.07.050
  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. Art. no. 6664996. P. 1–9. DOI: 10.1155/2020/6664996
  3. Dutta H., Basar F. A generalization of Orlicz sequence spaces by Cesàro mean of order one. Acta Math. Univ. Comenian, 2011. Vol. 80, No. 2. P. 185–200.
  4. Esi A., Bipin H., Esi A. New type of lacunary Orlicz difference sequence spaces generated by infinite matrices. Filomat, 2016. Vol. 30, No. 12. P. 3195–3208. DOI: 10.2298/FIL1612195E
  5. Et M., Çolak R. On some generalized sequence spaces. Soochow J. Math., 1995. Vol. 21, No. 4. P. 377–386.
  6. Et M., Lee P.Y., Tripathy B.C. Strongly almost (V,λ)(Λr)-summable sequences defined by Orlicz function. Hokkaido Math. J., 2006. Vol. 35. P. 197–213.
  7. Gupta M., Bhar A. Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals. Math. Slovaca, 2014. Vol. 64, No. 6. P. 1474–1496. DOI: 10.2478/s12175-014-0287-6
  8. Jebril I.H. A generalization of strongly Cesàro and strongly lacunary summable spaces. Acta Univ. Apalensis, 2010. Vol. 23. P. 49–61.
  9. Kizmaz H. On certain sequence spaces. Canad. Math. Bull., 1981. Vol. 24, No. 2. P. 169–176. DOI: 10.4153/CMB-1981-027-5
  10. Lindenstrauss J., Tzafriri L. On Orlicz sequence spaces. Israel J. Math., 1971. Vol. 10. P. 379–390. DOI: 10.1007/BF02771656
  11. Mursaleen M., Khan A.M., Qamaruddin. Difference sequence spaces defined by Orlicz functions. Demonstratio Math., 1999. Vol. 32, No. 1. P. 145–150. DOI: 10.1515/dema-1999-0115
  12. Nakano H. Modulared sequence spaces. Proc. Japan Acad., 1951. Vol. 27, No. 9. P. 508–512. DOI: 10.3792/pja/1195571225
  13. Orlicz W. Über Räume (LM). Bull. Int. Acad. Polon. Sci., 1936. P. 93–107. (in German)
  14. Tripathy B.C., Esi A. A new type of difference sequence spaces. Inter. J. Sci. Tech. 2006. Vol. 1, No. 1. P. 11–14.
  15. Tripathy B.C., Choudhary B., Sarma B. Some difference double sequence spaces defined by Orlicz function. Kyungpook Math. J., 2008. Vol. 48, No. 4. P. 613–622. DOI: 10.5666/KMJ.2008.48.4.613
  16. Tripathy B.C., Dutta H. Some difference paranormed sequence spaces defined by Orlicz functions. Fasc. Math., 2009. Vol. 42. P. 121–131.
  17. Tripathy B.C., Dutta H. On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary Δnm-statistical convergence. An. Ştiint. Univ. Ovidius Constanţa. Ser. Mat., 2012. Vol. 20. No. 1. P. 417–430.
  18. Woo J. On modular sequence spaces. Studia Math., 1973. Vol. 48. No. 3. P. 271–289.




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

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