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Year 2024, Volume: 7 Issue: 3, 1 - 12, 04.09.2024

Abstract

References

  • 1 I. J. Maddox, Elements of Functional Analysis , 2nded., The University Press, Cambridge, (1988).
  • 2 N. Nakano, Concave modulars, J. Math. Soc. Japan, 5(1953), 29-49.
  • 3 M. Mursaleen, and A. K. Noman, On some new difference sequence spaces of non-absolute type, Math. Comput. Mod., 52 (2010), pp. 603-617.
  • 4 W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978.
  • 5 S. Toeplitz,¨ Uber allegemeine Lineare mittelbildungen, Prace Math.¨ Fiz., 22 (1991). pp.113-119.
  • 6 A. Wilansky, Summability through Functional Analysis, North Holland Mathematics Studies, Amsterdam - New York - Oxford, (1984).
  • 7 Gupkari S.A., Some New Generalized Riesz Spaces, Fasciculi Mathematici, (2023).
  • 8 K. Raj and S.K Sharma., Difference Sequence Spaces Defined by A Sequence of Modulus Functions, Proyecciones Journal of Mathematics, (2011).
  • 9 G. M. Petersen, Regular matrix transformations, Mc Graw-Hill, London, (1966).
  • 10 N. A. Sheikh and A. H. Ganie, A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedago. Nygr., 28 (2012), pp. 47-58.
  • 11 C. S. Wang , On Nörlund sequence spaces, Tamkang J. Math., 9 (1978),¨ pp. 269-274.
  • 12 P. N. Ng and P. Y. Lee, Cesaro sequences spaces of non-absolute type,´ Comment. Math. Prace Mat. 20(2) (1978), pp. 429-433.
  • 13 K. G. Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180 (1993), pp. 223- 238.
  • 14 B. Altay, F. Başar and M. Mursaleen, On the Euler sequence spaces which include the spaces lp and l∞-II, Nonlinear Anal., 176 (2006), pp. 1465-1462. ,
  • 15 M. Başarır and M.Kayıkçı, On the Generalized m B -Riesz Difference Sequence Space and  -Property, (2009).

Generalized Riesz Spaces Defined by Using a Sequence of Modulus Functions

Year 2024, Volume: 7 Issue: 3, 1 - 12, 04.09.2024

Abstract

In this paper, we define a new Riesz sequence space using a sequence of modulus functions. Furthermore, we give that this space is linearly isomorphism with l(p) and determine its basis. We also give some inclusion relationships and compute α- and β- duals of this space.

References

  • 1 I. J. Maddox, Elements of Functional Analysis , 2nded., The University Press, Cambridge, (1988).
  • 2 N. Nakano, Concave modulars, J. Math. Soc. Japan, 5(1953), 29-49.
  • 3 M. Mursaleen, and A. K. Noman, On some new difference sequence spaces of non-absolute type, Math. Comput. Mod., 52 (2010), pp. 603-617.
  • 4 W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978.
  • 5 S. Toeplitz,¨ Uber allegemeine Lineare mittelbildungen, Prace Math.¨ Fiz., 22 (1991). pp.113-119.
  • 6 A. Wilansky, Summability through Functional Analysis, North Holland Mathematics Studies, Amsterdam - New York - Oxford, (1984).
  • 7 Gupkari S.A., Some New Generalized Riesz Spaces, Fasciculi Mathematici, (2023).
  • 8 K. Raj and S.K Sharma., Difference Sequence Spaces Defined by A Sequence of Modulus Functions, Proyecciones Journal of Mathematics, (2011).
  • 9 G. M. Petersen, Regular matrix transformations, Mc Graw-Hill, London, (1966).
  • 10 N. A. Sheikh and A. H. Ganie, A new paranormed sequence space and some matrix transformations, Acta Math. Acad. Paedago. Nygr., 28 (2012), pp. 47-58.
  • 11 C. S. Wang , On Nörlund sequence spaces, Tamkang J. Math., 9 (1978),¨ pp. 269-274.
  • 12 P. N. Ng and P. Y. Lee, Cesaro sequences spaces of non-absolute type,´ Comment. Math. Prace Mat. 20(2) (1978), pp. 429-433.
  • 13 K. G. Erdmann, Matrix transformations between the sequence spaces of Maddox, J. Math. Anal. Appl., 180 (1993), pp. 223- 238.
  • 14 B. Altay, F. Başar and M. Mursaleen, On the Euler sequence spaces which include the spaces lp and l∞-II, Nonlinear Anal., 176 (2006), pp. 1465-1462. ,
  • 15 M. Başarır and M.Kayıkçı, On the Generalized m B -Riesz Difference Sequence Space and  -Property, (2009).
There are 15 citations in total.

Details

Primary Language English
Subjects Numerical Analysis
Journal Section Research Articles
Authors

Emine Özçelik 0000-0001-9203-6550

Çiğdem Bektaş 0000-0003-0397-3193

Publication Date September 4, 2024
Submission Date April 4, 2024
Acceptance Date July 24, 2024
Published in Issue Year 2024 Volume: 7 Issue: 3

Cite

APA Özçelik, E., & Bektaş, Ç. (2024). Generalized Riesz Spaces Defined by Using a Sequence of Modulus Functions. Journal of Advanced Mathematics and Mathematics Education, 7(3), 1-12.