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ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX

Year 2020, Volume 3, Issue 1, 66 - 76, 31.01.2020
https://doi.org/10.33773/jum.679809

Abstract

In this study, we give some new FK-spaces by means of an infinite matrix as an operator and define some new beta and gama type duality of sequence spaces [3, 4]. We also introduce some new sections and investigate some properties like AB-, FAK-, SAK- and AK- in an FK-space. By this way, we obtain some new distinguished subspaces of an FK- space [5]. Among other results, we prove that the sum of infinite numbers of FK-spaces and the intersection of a sequence of FK-spaces which have these new properties with corresponding paranorms have also these new properties. The reader can refer to [1], [2] and [11] for the main results and related topics in FK-space theory.

References

  • F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, (2012).
  • J. Boos, Classical and Modern Methods in Summability, Oxford University Press. New York, (2000).
  • M. Buntinas, Convergent and bounded Cesaro sections in FK-spaces, Math. Z., Vol. 121, pp. 191-200 (1971).
  • M. Buntinas, On Toeplitz sections in sequence spaces, Math. Proc. Cambridge Philos. Soc., Vol. 78, pp. 451-460 (1975).
  • İ. Dağadur, On some subspaces of an FK-space, Math. Commun., Vol.7, pp. 15-20 (2002).
  • R. Devos, Combinations of distinguished subsets and conullity, Math. Z., Vol. 192, pp. 447-451 (1986).
  • D. J. Fleming and J. C. Magee, FK-multiplier spaces, Proc. Amer. Math. Soc., Vol. 125, N. 1, pp. 175-181 (1997).
  • D. J. H. Garling, The beta and gama duality of sequence spaces, Proc. Cambridge Philos. Soc., Vol. 63, pp. 963-981 (1967).
  • M. Mursaleen A. K. Noman, On the spaces of lamda convergent and bounded sequences, Thai J. Math., Vol. 8, N. 2, pp. 311-329 (2010).
  • W. H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, (1981).
  • A. Wilansky, Summability Through Functional Analysis, North-Holland, Amsterdam, (1984).
  • K. Zeller, Allgemeine eigenschaften von limitierungsverfahren, Math. Z., Vol. 53, pp. 463-487 (1951).

Year 2020, Volume 3, Issue 1, 66 - 76, 31.01.2020
https://doi.org/10.33773/jum.679809

Abstract

References

  • F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, (2012).
  • J. Boos, Classical and Modern Methods in Summability, Oxford University Press. New York, (2000).
  • M. Buntinas, Convergent and bounded Cesaro sections in FK-spaces, Math. Z., Vol. 121, pp. 191-200 (1971).
  • M. Buntinas, On Toeplitz sections in sequence spaces, Math. Proc. Cambridge Philos. Soc., Vol. 78, pp. 451-460 (1975).
  • İ. Dağadur, On some subspaces of an FK-space, Math. Commun., Vol.7, pp. 15-20 (2002).
  • R. Devos, Combinations of distinguished subsets and conullity, Math. Z., Vol. 192, pp. 447-451 (1986).
  • D. J. Fleming and J. C. Magee, FK-multiplier spaces, Proc. Amer. Math. Soc., Vol. 125, N. 1, pp. 175-181 (1997).
  • D. J. H. Garling, The beta and gama duality of sequence spaces, Proc. Cambridge Philos. Soc., Vol. 63, pp. 963-981 (1967).
  • M. Mursaleen A. K. Noman, On the spaces of lamda convergent and bounded sequences, Thai J. Math., Vol. 8, N. 2, pp. 311-329 (2010).
  • W. H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, (1981).
  • A. Wilansky, Summability Through Functional Analysis, North-Holland, Amsterdam, (1984).
  • K. Zeller, Allgemeine eigenschaften von limitierungsverfahren, Math. Z., Vol. 53, pp. 463-487 (1951).

Details

Primary Language English
Subjects Mathematics
Journal Section Research Article
Authors

Mahmut KARAKUŞ
VAN YÜZÜNCÜ YIL ÜNİVERSİTESİ
0000-0002-4468-629X
Türkiye


Tunay BİLGİN
YÜZÜNCÜ YIL ÜNİVERSİTESİ
Türkiye

Publication Date January 31, 2020
Application Date January 24, 2020
Acceptance Date March 2, 2020
Published in Issue Year 2020, Volume 3, Issue 1

Cite

Bibtex @research article { jum679809, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2020}, volume = {3}, pages = {66 - 76}, doi = {10.33773/jum.679809}, title = {ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX}, key = {cite}, author = {Karakuş, Mahmut and Bilgin, Tunay} }
APA Karakuş, M. & Bilgin, T. (2020). ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX . Journal of Universal Mathematics , 3 (1) , 66-76 . DOI: 10.33773/jum.679809
MLA Karakuş, M. , Bilgin, T. "ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX" . Journal of Universal Mathematics 3 (2020 ): 66-76 <https://dergipark.org.tr/en/pub/jum/issue/52380/679809>
Chicago Karakuş, M. , Bilgin, T. "ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX". Journal of Universal Mathematics 3 (2020 ): 66-76
RIS TY - JOUR T1 - ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX AU - Mahmut Karakuş , Tunay Bilgin Y1 - 2020 PY - 2020 N1 - doi: 10.33773/jum.679809 DO - 10.33773/jum.679809 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 66 EP - 76 VL - 3 IS - 1 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.679809 UR - https://doi.org/10.33773/jum.679809 Y2 - 2020 ER -
EndNote %0 Journal of Universal Mathematics ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX %A Mahmut Karakuş , Tunay Bilgin %T ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX %D 2020 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 3 %N 1 %R doi: 10.33773/jum.679809 %U 10.33773/jum.679809
ISNAD Karakuş, Mahmut , Bilgin, Tunay . "ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX". Journal of Universal Mathematics 3 / 1 (January 2020): 66-76 . https://doi.org/10.33773/jum.679809
AMA Karakuş M. , Bilgin T. ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX. JUM. 2020; 3(1): 66-76.
Vancouver Karakuş M. , Bilgin T. ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX. Journal of Universal Mathematics. 2020; 3(1): 66-76.
IEEE M. Karakuş and T. Bilgin , "ON SOME NEW FK SPACES OBTAINED FROM SUMMABILITY MATRIX", Journal of Universal Mathematics, vol. 3, no. 1, pp. 66-76, Jan. 2020, doi:10.33773/jum.679809