Orlicz Extension of New Sequence Spaces Engendered by the Composition of Binomial Matrix and Double Band Matrix

Jamwal, Seema; Sharma, Sonali; Raj, Kuldip; Sharma, Sunil K.; Bashir, Runda A. A.; Mahgoub, Hala S.; Gouni, Albasha A.; Bakery, Awad A.

doi:10.28924/2291-8639-22-2024-177

Research Article

Orlicz Extension of New Sequence Spaces Engendered by the Composition of Binomial Matrix and Double Band Matrix

Seema Jamwal
Sonali Sharma
Kuldip Raj
Sunil K. Sharma
Runda A. A. Bashir
Hala S. Mahgoub
Albasha A. Gouni
Awad A. Bakery*

* Corresponding author

Abstract

The present paper is emphasis on introducing Orlicz extension of new sequence spaces (i.e b^r,s₀(M,G), b^r,s_c(M,G) and b^r,s_∞(M,G)) by way of the composition of binomial matrix and double band matrix, which are BK-spaces, moreover we prove that these spaces are linearly isomorphic to the spaces l∞, c0 and c. We also derive some inclusion relations. Additionally, we find the Schauder basis for these spaces and finally we also determine the α−, β− and γ− duals of these spaces.

How to Cite

S. Jamwal, S. Sharma, K. Raj, S. K. Sharma, R. A. A. Bashir, H. S. Mahgoub, A. A. Gouni, A. A. Bakery, Orlicz Extension of New Sequence Spaces Engendered by the Composition of Binomial Matrix and Double Band Matrix, Int. J. Anal. Appl. 22 (2024), 177. https://doi.org/10.28924/2291-8639-22-2024-177

BibTeX

@article{Jamwal2024,
  author  = {Jamwal, Seema and Sharma, Sonali and Raj, Kuldip and Sharma, Sunil K. and Bashir, Runda A. A. and Mahgoub, Hala S. and Gouni, Albasha A. and Bakery, Awad A.},
  title   = {Orlicz Extension of New Sequence Spaces Engendered by the Composition of Binomial Matrix and Double Band Matrix},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {177},
  doi     = {10.28924/2291-8639-22-2024-177}
}

References

[1] B. Altay, F. Basar, On Some Euler Sequence Spaces of Nonabsolute Type, Ukr. Math. J. 57 (2005), 1–17. https://doi.org/10.1007/s11253-005-0168-9.
[2] B. Altay, F. Ba¸sar, M. Mursaleen, On the Euler Sequence Spaces Which Include the Spaces `p and `∞, Inf. Sci. 176 (2006), 1450–1462. https://doi.org/10.1016/j.ins.2005.05.008.
[3] B. Altay, H. Polat, On Some New Euler Difference Sequence Spaces, Southeast Asian Bull. Math. 30 (2006), 209–220.
[4] M.C. Bi¸sgin, The Binomial Sequence Spaces of Nonabsolute Type, J. Ineq. Appl. 2016 (2016), 309. https://doi.org/10.1186/s13660-016-1256-0.
[5] M.C. Bi¸sgin, The Binomial Almost Convergent and Null Sequence Spaces, Comm. Fac. Sci. Univ. Ankara Ser. A1. Math. Stat. 67 (2018), 211–224. https://doi.org/10.1501/commua1_0000000843.
[6] M.C. Bi¸sgin, A. Sönmez, Two New Sequence Spaces Generated by the Composition of M Th Order Generalized Difference Matrix and Lambda Matrix, J. Ineq. Appl. 2014 (2014), 274. https://doi.org/10.1186/1029-242x-2014-274.
[7] M.C. Bi¸sgin, Some Notes on the Sequence Spaces l λ p (G m) and l λ ∞(G m), GU J. Sci. 30 (2017), 381–393.
[8] F. Ba¸sar, B. Altay, On the Space of Sequences of P-Bounded Variation and Related Matrix Mappings, Ukr. Math. J. 55 (2003), 136–147. https://doi.org/10.1023/a:1025080820961.
[9] B. Choudhary, S. Nanda, Functional Analysis with Applications, Wiley, 1989.
[10] M. Et, On Some Difference Sequence Spaces, Turk. J. Math. 17 (1993), 18–24.
[11] E.E. Kara, M. Ba¸sarir, On Compact Operators and Some Euler B (m) -Difference Sequence Spaces, J. Math. Anal. Appl. 379 (2011), 499–511. https://doi.org/10.1016/j.jmaa.2011.01.028.
[12] V. Karakaya, H. Polat, Some New Paranormed Sequence Spaces Defined by Euler and Difference Operators, Acta Sci. Math. 76 (2010), 87–100. https://doi.org/10.1007/bf03549822.
[13] M. Kiri¸sçi, F. Ba¸sar, Some New Sequence Spaces Derived by the Domain of Generalized Difference Matrix, Comp. Math. Appl. 60 (2010), 1299–1309. https://doi.org/10.1016/j.camwa.2010.06.010.
[14] H. Kizmaz, On Certain Sequence Spaces, Can. Math. Bull. 24 (1981), 169–176. https://doi.org/10.4153/cmb-1981-027-5.
[15] J. Lindenstrauss, L. Tzafriri, On Orlicz Sequence Spaces, Israel J. Math. 10 (1971), 379–390. https://doi.org/10.1007/bf02771656.
[16] J. Meng, M. Song, Binomial Difference Sequence Spaces of Order m, Adv. Diff. Equ. 2017 (2017), 241. https://doi.org/10.1186/s13662-017-1291-2.
[17] P.N. Ng, P.Y. Lee, Cesàro Sequence Spaces of Non–absolute Type, Comment. Math. (Prace Mat.) 20 (1978), 429–433.
[18] H. Polat, F. Ba¸sar, Some Euler Spaces of Difference Sequences of Order m, Acta Math. Sci. 27 (2007), 254–266. https://doi.org/10.1016/s0252-9602(07)60024-1.
[19] M. Stieglitz, H. Tietz, Matrix Transformationen von Folgenräumen eine Ergebnisübersicht, Math. Z. 154 (1977), 1–16. https://doi.org/10.1007/bf01215107.
[20] A. Sönmez, Some New Sequence Spaces Derived by the Composition of Binomial Matrix and Double Band Matrix, J. Appl. Anal. Comp. 9 (2019), 231–244. https://doi.org/10.11948/2019.231.
[21] C.S. Wang, On Nörlund Sequence Spaces. Tamkang J. Math. 9 (1978), 269–274.
[22] A. Wilansky, Summability Throught Functional Analysis, North-Holland Mathematics Studies, Elsevier, 1984.