AIMS Mathematics, 2020, 5(4): 2858-2868. doi: 10.3934/math.2020183

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Distinguished subspaces in topological sequence spaces theory

Department of Mathematics, Kahramanmaraş Sütçü İmam University, Kahramanmaraş-46100, Turkey

In this paper, we study $R_{\lambda}$-semiconservative $FK$-spaces for Riesz-method defined by the Riesz matrix $(R)$ and give some characterizations. We show that if $\ell_{A}$ is $\ell$-replaceable, then $A$ can not be $R_{\lambda}$-semiconservative and also if $X_{A}$ is $R_{\lambda}$-conull $FK$-space then it must be $R_{\lambda}$-semiconservative space. In addition, we determine a new $r(\lambda)$ and $rb(\lambda)$ type duality of a sequence space $X$ containing $\varphi$. The paper aims to develop some new subspaces which each one has its own value on topological sequence spaces theory. These subspaces are called as $R_{\lambda}S; R_{\lambda}W; R_{\lambda}F^{+};$ and $R_{\lambda}B^{+}$ for a locally convex $FK$-space X containing $\varphi$. The subspaces mentioned in the work requires some serious studies and they arose independently from the literature which was done at the recent stage of the development of summability through functional analysis.
  Figure/Table
  Supplementary
  Article Metrics

References

1. J. Boos, Classical and Modern Methods in Summability, Oxford University Press, New York, Oxford, 2000.

2. A. Wilansky, Summability Through Funtional Analysis, North Holland, 1984.

3. A. Wilansky, Functional Analysis, Blaisdell Press, 1964.

4. K. Zeller, Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z., 53 (1951), 463-487.    

5. K. Zeller, Theorie der Limitierungsverfahren, Berlin-Heidelberg New York, 1958.

6. I. Dağadur, Cλ-conull FK-spaces, Demonstr. Math., 35 (2002), 835-848.

7. J. A. Osikiewicz, Equivalance results for Cesàro submethods, Analysis, 20 (2000), 35-43.

8. S. A. Mohiuddine, A. Alotaibi, Weighted almost convergence and related infinite matrices, J. Inequal. Appl., 2018 (2018), 15.

9. A. K. Snyder, A. Wilansky, Inclusion Theorems and Semiconservative FK spaces, Rocky Mtn. J. Math., 2 (1972), 595-603.    

10. H. G. Ince, Cesàro semiconservative FK-Spaces, Math. Communs., 14 (2009), 157-165.

11. I. Dağadur, Cλ semiconservative FK-Spaces, Ukr. Math. J., 64 (2012), 908-918.

12. U. Değer, On Approximation by Nörlund And Riesz Submethods in Variable Expotent Lebesgue Spaces, Commun. Fac. Sci. Univ. Ank. Series A1, 67 (2018), 46-67.

13. M. Buntinas, Convergent and bounded Cesaro sections in FK-space, Math. Z., 121 (1971), 191-200.    

14. G. Goes, S. Goes, Sequence of bounded variations and sequences of Fourier coefficients I., Math. Z., 118 (1970), 93-102.    

15. M. Temizer Ersoy, B. Altay, H. Furkan, On Riesz Sections in Sequence Spaces, Adv. Math. Compt. Sci., 24 (2017), 1-10.

16. M. S. Macphail, C. Orhan, Some Properties of Absolute Summability Domains, Analysis, 9 (1989), 317-322.

17. E. Malkowsky, F. Başar, A Survey On Some Paranormed Sequence Spaces, Filomat, 31 (2017), 1099-1122.    

18. A. Malkowsky, F. Özger, V. Veličković, Matrix Transformations on Mixed Paranorm Spaces, Filomat, 31 (2017), 2957-2966.    

19. H. B. Ellidokuzoglu, S. Demiriz, Euler-Riesz Difference Sequence Spaces, Turk. J. Math. Comput. Sci., 7 (2017), 63-72.

20. F. Gökçe, M. A. Sarıgöl, Generalization of the Absolute Cesàro Space and Some Matrix Transformations, Numer. Func. Anal. Opt., 40 (2019), 1039-1052.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved