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

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-177
Published: Oct 2, 2024
Cite as:
Seema Jamwal, Sonali Sharma, Kuldip Raj, Sunil K. Sharma, Runda A. A. Bashir, Hala S. Mahgoub, Albasha A. Gouni, Awad 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.

Main Article Content

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

Abstract

The present paper is emphasis on introducing Orlicz extension of new sequence spaces (i.e br,s0(M,G), br,sc(M,G) and br,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.

Article Details

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.