Research Article
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Year 2020, Volume: 33 Issue: 2, 476 - 490, 01.06.2020
https://doi.org/10.35378/gujs.522691

Abstract

References

  • 1. Choudhary, B, Nanda, S: Functional Analysis with Applications. Wiley, New Delhi (1989).
  • 2.Wilansky, A: Summability Through Functional Analysis. North-Holland Mathematics Studies, vol. 85. Elsevier, Amsterdam (1984).
  • 3. Wang, C-S: On Norlund sequence spaces. Tamkang J. Math. 9, 269-274 (1978).
  • 4. Ng, P-N, Lee, P-Y: Cesaro sequence spaces of non-absolute type. Comment. Math. (Prace Mat.) 20(2), 429-433 (1978).
  • 5. Kızmaz, H: On certain sequence spaces. Canad. Math. Bull. 24(2), 169-176 (1981).
  • 6. Et, M: On some difference sequence spaces. Turkish J. Math., 17, 18-24 (1993).
  • 7. Altay, B, Başar, F: Some Euler sequence spaces of non-absolute type. Ukr. Math. J. 57(1), 1-17 (2005).
  • 8. Altay, B, Başar, F, Mursaleen, M: On the Euler sequence spaces which include the spaces l_p and l_∞ I. Inf. Sci. 176(10), 1450-1462 (2006).
  • 9. Mursaleen, M, Başar, F, Altay, B: On the Euler sequence spaces which include the spaces l_p and l_∞ II. Nonlinear Anal. 65(3), 707-717 (2006).
  • 10. Altay, B, Polat, H: On some new Euler difference sequence spaces. Southeast Asian Bull. Math. 30(2), 209-220 (2006).
  • 11. Polat, H, Başar, F: Some Euler spaces of difference sequences of order m. Acta Math. Sci. Ser. B, Engl. Ed. 27B(2), 254-266 (2007).
  • 12. Kara, EE, Başarır, M: On compact operators and some Euler B^((m))-difference sequence spaces. J. Math. Anal. Appl. 379(2), 499-511 (2011).
  • 13. Kirişçi, M, Başar, F: Some new sequence spaces derived by the domain of generalized difference matrix. Comput. Math. Appl. 60(5), 1299-1309 (2010).
  • 14. Bişgin, MC: The Binomial sequence spaces of nonabsolute type. J. Inequal. Appl., 2016:309,(2016).
  • 15. Bişgin, MC: The Binomial sequence spaces which include the spaces l_p and l_∞ and geometric properties. J. Inequal. Appl., 2016:304, (2016).
  • 16. Jarrah, AM, Malkowsky, E: BK-spaces, bases and linear operators. Rend. Circ. Mat. Palermo, 52(2), 177-191 (1998).
  • 17. Stieglitz, M, Tietz, H: Matrix Transformationen von Folgenräumen eine ergebnisübersicht. Math. Z. 154, 1-16 (1977).
  • 18. Bişgin, MC: A note on the sequence space b_p^(r,s) (G). Cumhuriyet Sci. J., 38(4), 11-25 (2017).

Some Notes on the New Sequence Space b_p^(r,s) (D)

Year 2020, Volume: 33 Issue: 2, 476 - 490, 01.06.2020
https://doi.org/10.35378/gujs.522691

Abstract

In this paper, we describe the sequence space b_p^(r,s) (D) originated by the composition of the Binomial matrix and generalized second order difference (triple band) matrix and indicate that the space b_p^(r,s) (D) is linearly isomorphic to the space l_p, where 1≤p<∞. Moreover, we obtain some inclusion relations and Schauder basis of the space b_p^(r,s) (D). We also pinpoint α-, β- and γ-duals of the space b_p^(r,s) (D). Finally, we classify some matrix classes related to the space b_p^(r,s) (D).

References

  • 1. Choudhary, B, Nanda, S: Functional Analysis with Applications. Wiley, New Delhi (1989).
  • 2.Wilansky, A: Summability Through Functional Analysis. North-Holland Mathematics Studies, vol. 85. Elsevier, Amsterdam (1984).
  • 3. Wang, C-S: On Norlund sequence spaces. Tamkang J. Math. 9, 269-274 (1978).
  • 4. Ng, P-N, Lee, P-Y: Cesaro sequence spaces of non-absolute type. Comment. Math. (Prace Mat.) 20(2), 429-433 (1978).
  • 5. Kızmaz, H: On certain sequence spaces. Canad. Math. Bull. 24(2), 169-176 (1981).
  • 6. Et, M: On some difference sequence spaces. Turkish J. Math., 17, 18-24 (1993).
  • 7. Altay, B, Başar, F: Some Euler sequence spaces of non-absolute type. Ukr. Math. J. 57(1), 1-17 (2005).
  • 8. Altay, B, Başar, F, Mursaleen, M: On the Euler sequence spaces which include the spaces l_p and l_∞ I. Inf. Sci. 176(10), 1450-1462 (2006).
  • 9. Mursaleen, M, Başar, F, Altay, B: On the Euler sequence spaces which include the spaces l_p and l_∞ II. Nonlinear Anal. 65(3), 707-717 (2006).
  • 10. Altay, B, Polat, H: On some new Euler difference sequence spaces. Southeast Asian Bull. Math. 30(2), 209-220 (2006).
  • 11. Polat, H, Başar, F: Some Euler spaces of difference sequences of order m. Acta Math. Sci. Ser. B, Engl. Ed. 27B(2), 254-266 (2007).
  • 12. Kara, EE, Başarır, M: On compact operators and some Euler B^((m))-difference sequence spaces. J. Math. Anal. Appl. 379(2), 499-511 (2011).
  • 13. Kirişçi, M, Başar, F: Some new sequence spaces derived by the domain of generalized difference matrix. Comput. Math. Appl. 60(5), 1299-1309 (2010).
  • 14. Bişgin, MC: The Binomial sequence spaces of nonabsolute type. J. Inequal. Appl., 2016:309,(2016).
  • 15. Bişgin, MC: The Binomial sequence spaces which include the spaces l_p and l_∞ and geometric properties. J. Inequal. Appl., 2016:304, (2016).
  • 16. Jarrah, AM, Malkowsky, E: BK-spaces, bases and linear operators. Rend. Circ. Mat. Palermo, 52(2), 177-191 (1998).
  • 17. Stieglitz, M, Tietz, H: Matrix Transformationen von Folgenräumen eine ergebnisübersicht. Math. Z. 154, 1-16 (1977).
  • 18. Bişgin, MC: A note on the sequence space b_p^(r,s) (G). Cumhuriyet Sci. J., 38(4), 11-25 (2017).
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Abdulcabbar Sönmez 0000-0003-2142-0736

Publication Date June 1, 2020
Published in Issue Year 2020 Volume: 33 Issue: 2

Cite

APA Sönmez, A. (2020). Some Notes on the New Sequence Space b_p^(r,s) (D). Gazi University Journal of Science, 33(2), 476-490. https://doi.org/10.35378/gujs.522691
AMA Sönmez A. Some Notes on the New Sequence Space b_p^(r,s) (D). Gazi University Journal of Science. June 2020;33(2):476-490. doi:10.35378/gujs.522691
Chicago Sönmez, Abdulcabbar. “Some Notes on the New Sequence Space b_p^(r,s) (D)”. Gazi University Journal of Science 33, no. 2 (June 2020): 476-90. https://doi.org/10.35378/gujs.522691.
EndNote Sönmez A (June 1, 2020) Some Notes on the New Sequence Space b_p^(r,s) (D). Gazi University Journal of Science 33 2 476–490.
IEEE A. Sönmez, “Some Notes on the New Sequence Space b_p^(r,s) (D)”, Gazi University Journal of Science, vol. 33, no. 2, pp. 476–490, 2020, doi: 10.35378/gujs.522691.
ISNAD Sönmez, Abdulcabbar. “Some Notes on the New Sequence Space b_p^(r,s) (D)”. Gazi University Journal of Science 33/2 (June 2020), 476-490. https://doi.org/10.35378/gujs.522691.
JAMA Sönmez A. Some Notes on the New Sequence Space b_p^(r,s) (D). Gazi University Journal of Science. 2020;33:476–490.
MLA Sönmez, Abdulcabbar. “Some Notes on the New Sequence Space b_p^(r,s) (D)”. Gazi University Journal of Science, vol. 33, no. 2, 2020, pp. 476-90, doi:10.35378/gujs.522691.
Vancouver Sönmez A. Some Notes on the New Sequence Space b_p^(r,s) (D). Gazi University Journal of Science. 2020;33(2):476-90.