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The space $bv_{k}^{\theta }$ and matrix transformations

Year 2019, Volume: 2 Issue: 3, 169 - 172, 30.12.2019

G. Canan Hazar Güleç Mehmet Ali Sarıgöl

Abstract

In this study, we introduce the space $bv_{k}^{\theta },$ give its some algebraic and topological properties, and also characterize some matrix operators defined on that space. Also we extend some well known results.

Keywords

BK spaces Matrix transformations Sequence spaces

Supporting Institution

Pamukkale University Scientific Research Projects Coordinatorship

Project Number

(Grant No. 2019KRM004-029)

References

  • [1] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematical Studies, 85, Elsevier Science Publisher, 1984.
  • [2] A. M. Akhmedov, F. Başar, The fine spectra of the difference operator $\Delta $ over the sequence space $b{v_p},(1 \le p < \infty ),$ Acta Math. Sin. (Engl. Ser.), 23(10) (2007), 1757-1768.
  • [3] F. Başar, B. Altay, M. Mursaleen, Some generalizations of the space bvp of p-bounded variation sequences, Nonlinear Analysis 68(2) (2008), 273–287.
  • [4] G.C.H. Güleç, Compact Matrix Operators on Absolute Cesàro Spaces, Numer. Funct. Anal. Optim., 2019. DOI: 10.1080/01630563.2019.1633665
  • [5] G. C. Hazar, M.A. Sarıgöl, On absolute Nörlund spaces and matrix operators, Acta Math. Sin. (Engl. Ser.), 34(5) (2018), 812-826.
  • [6] A. M. Jarrah, E. Malkowsky, BK spaces, bases and linear operators, Rend. Circ. Mat. Palermo II, 52 (1998), 177-191.
  • [7] E. E. Kara, M. ˙Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear Algebra 64 (2016), 2208–2223.
  • [8] M. A. Sarıgöl, Spaces of Series Summable by Absolute Cesàro and Matrix Operators, Comm. Math Appl. 7(1) (2016), 11-22.
  • [9] I. J. Maddox, Elements of functinal analysis, Cambridge University Press, London, New York, (1970).
  • [10] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenraumen Eine Ergebnisüberischt, Math Z. 154 (1977), 1-16.
  • [11] E. Malkowsky, V. Rakocevic, S. Živkovic, Matrix transformations between the sequence space bvk and certain BK spaces, Bull. Cl. Sci. Math. Nat. Sci. Math. 123(27) (2002), 33–46.
  • [12] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford 18(2) (1967), 345-355.
  • [13] M. F. Mears, Absolute Regularity and the Nörlund Mean, Annals of Math., 38(3) (1937), 594-601.

Year 2019, Volume: 2 Issue: 3, 169 - 172, 30.12.2019

G. Canan Hazar Güleç Mehmet Ali Sarıgöl

Abstract

Project Number

(Grant No. 2019KRM004-029)

References

  • [1] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematical Studies, 85, Elsevier Science Publisher, 1984.
  • [2] A. M. Akhmedov, F. Başar, The fine spectra of the difference operator $\Delta $ over the sequence space $b{v_p},(1 \le p < \infty ),$ Acta Math. Sin. (Engl. Ser.), 23(10) (2007), 1757-1768.
  • [3] F. Başar, B. Altay, M. Mursaleen, Some generalizations of the space bvp of p-bounded variation sequences, Nonlinear Analysis 68(2) (2008), 273–287.
  • [4] G.C.H. Güleç, Compact Matrix Operators on Absolute Cesàro Spaces, Numer. Funct. Anal. Optim., 2019. DOI: 10.1080/01630563.2019.1633665
  • [5] G. C. Hazar, M.A. Sarıgöl, On absolute Nörlund spaces and matrix operators, Acta Math. Sin. (Engl. Ser.), 34(5) (2018), 812-826.
  • [6] A. M. Jarrah, E. Malkowsky, BK spaces, bases and linear operators, Rend. Circ. Mat. Palermo II, 52 (1998), 177-191.
  • [7] E. E. Kara, M. ˙Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear and Multilinear Algebra 64 (2016), 2208–2223.
  • [8] M. A. Sarıgöl, Spaces of Series Summable by Absolute Cesàro and Matrix Operators, Comm. Math Appl. 7(1) (2016), 11-22.
  • [9] I. J. Maddox, Elements of functinal analysis, Cambridge University Press, London, New York, (1970).
  • [10] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenraumen Eine Ergebnisüberischt, Math Z. 154 (1977), 1-16.
  • [11] E. Malkowsky, V. Rakocevic, S. Živkovic, Matrix transformations between the sequence space bvk and certain BK spaces, Bull. Cl. Sci. Math. Nat. Sci. Math. 123(27) (2002), 33–46.
  • [12] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford 18(2) (1967), 345-355.
  • [13] M. F. Mears, Absolute Regularity and the Nörlund Mean, Annals of Math., 38(3) (1937), 594-601.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

G. Canan Hazar Güleç 0000-0002-8825-5555

Mehmet Ali Sarıgöl 0000-0002-4107-4669

Project Number (Grant No. 2019KRM004-029)
Publication Date December 30, 2019
Acceptance Date December 2, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Hazar Güleç, G. C., & Sarıgöl, M. A. (2019). The space $bv_{k}^{\theta }$ and matrix transformations. Conference Proceedings of Science and Technology, 2(3), 169-172.
AMA Hazar Güleç GC, Sarıgöl MA. The space $bv_{k}^{\theta }$ and matrix transformations. Conference Proceedings of Science and Technology. December 2019;2(3):169-172.
Chicago Hazar Güleç, G. Canan, and Mehmet Ali Sarıgöl. “The Space $bv_{k}^{\theta }$ and Matrix Transformations”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 169-72.
EndNote Hazar Güleç GC, Sarıgöl MA (December 1, 2019) The space $bv_{k}^{\theta }$ and matrix transformations. Conference Proceedings of Science and Technology 2 3 169–172.
IEEE G. C. Hazar Güleç and M. A. Sarıgöl, “The space $bv_{k}^{\theta }$ and matrix transformations”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 169–172, 2019.
ISNAD Hazar Güleç, G. Canan - Sarıgöl, Mehmet Ali. “The Space $bv_{k}^{\theta }$ and Matrix Transformations”. Conference Proceedings of Science and Technology 2/3 (December 2019), 169-172.
JAMA Hazar Güleç GC, Sarıgöl MA. The space $bv_{k}^{\theta }$ and matrix transformations. Conference Proceedings of Science and Technology. 2019;2:169–172.
MLA Hazar Güleç, G. Canan and Mehmet Ali Sarıgöl. “The Space $bv_{k}^{\theta }$ and Matrix Transformations”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 169-72.
Vancouver Hazar Güleç GC, Sarıgöl MA. The space $bv_{k}^{\theta }$ and matrix transformations. Conference Proceedings of Science and Technology. 2019;2(3):169-72.
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