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Year 2018, Volume: 1 Issue: 1, 61 - 68, 30.06.2018
https://doi.org/10.33401/fujma.409932

Abstract

References

  • [1] B. Choudhary and S. Nanda, Functional Analysis with Applications, Wiley, New Delhi, 1989.
  • [2] M. Kirisçi, On the Taylor Sequence Spaces of Non-Absolute Type which Include The Spaces c0 and c, Journal of Math. Analysis 6 (2015), 22-35.
  • [3] B. Altay, F. Başar, Some Euler Sequence Spaces of Non-Absolute Type, Ukrainian Math. J. 57 (2005), 1-17.
  • [4] M. Şengönül, F. Başar, Some New Cesaro Sequence Spaces of Non-Absolute Type which Include The Spaces c0 and c, Soochow J. Math. 31 (2005), 107-119.
  • [5] B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include in the spaces lp and l, Inform. Sci. 176 (2006), 1450-1462.
  • [6] E. Malkowsky, Recent results in the theory of matrix transformations in sequences spaces, Mat. Vesnik 49 (1997), 187-196.
  • [7] P. N. Ng, P. Y. Lee, Cesaro sequences spaces of non-absolute type, Comment. Math. Prace Mat. 20 (1978), 429-433.
  • [8] C. S. Wang, On Norlund seqence spaces, Tamkang J. Math. 9 (1978), 269-274.
  • [9] G. H. Lawden, Pascal matrices, Mathematical Gazette 56 (1972), 325-327.
  • [10] S. Dutta and P. Baliarsingh, On some Toeplitz matrices and their inversions, J. Egypt Math. Soc. 22 (2014), 420-423.
  • [11] R. Brawer, Potenzen der Pascal matrix und eine Identitat der Kombinatorik, Elem. der Math. 45 (1990), 107-110.
  • [12] A. Edelman and G. Strang, Pascal Matrices, The Mathematical Association of America, Monthly 111 (2004), 189-197.
  • [13] C. Lay David, Linear Algebra and Its Applications, 4th Ed. Boston, Pearson, Addison-Wesley, 2012.
  • [14] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, Cambridge, 1981.
  • [15] D.J.H. Garling, The α, β and γ Duality of Sequence Spaces, Proc. Comb. Phil. Soc. 63 (1967), 963-981.
  • [16] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenraumen Eine Ergebnis¨ubersict, Math. Z. 154 (1977), 1-16.

Some new Pascal sequence spaces

Year 2018, Volume: 1 Issue: 1, 61 - 68, 30.06.2018
https://doi.org/10.33401/fujma.409932

Abstract

The main purpose of the present paper is to study of some new Pascal sequence spaces $p_{\infty }$, $p_{c}$ and $p_{0}$. New Pascal sequence spaces $p_{\infty }$, $p_{c}$ and $p_{0}$ are found as $BK$-spaces and it is proved that the spaces $% p_{\infty }$, $p_{c}$ and $p_{0}~$are linearly isomorphic to the spaces $% l_{\infty }$, $c\ $and $c_{0}$ respectively. Afterward, $\alpha $-, $\beta $% -~and $\gamma $-duals of these spaces $p_{c}$ and $p_{0}$ are computed and their bases are consructed. Finally, matrix the classes $(p_{c}:l_{p})$ and $% (p_{c}:c)$ have been characterized.

References

  • [1] B. Choudhary and S. Nanda, Functional Analysis with Applications, Wiley, New Delhi, 1989.
  • [2] M. Kirisçi, On the Taylor Sequence Spaces of Non-Absolute Type which Include The Spaces c0 and c, Journal of Math. Analysis 6 (2015), 22-35.
  • [3] B. Altay, F. Başar, Some Euler Sequence Spaces of Non-Absolute Type, Ukrainian Math. J. 57 (2005), 1-17.
  • [4] M. Şengönül, F. Başar, Some New Cesaro Sequence Spaces of Non-Absolute Type which Include The Spaces c0 and c, Soochow J. Math. 31 (2005), 107-119.
  • [5] B. Altay, F. Başar, M. Mursaleen, On the Euler sequence spaces which include in the spaces lp and l, Inform. Sci. 176 (2006), 1450-1462.
  • [6] E. Malkowsky, Recent results in the theory of matrix transformations in sequences spaces, Mat. Vesnik 49 (1997), 187-196.
  • [7] P. N. Ng, P. Y. Lee, Cesaro sequences spaces of non-absolute type, Comment. Math. Prace Mat. 20 (1978), 429-433.
  • [8] C. S. Wang, On Norlund seqence spaces, Tamkang J. Math. 9 (1978), 269-274.
  • [9] G. H. Lawden, Pascal matrices, Mathematical Gazette 56 (1972), 325-327.
  • [10] S. Dutta and P. Baliarsingh, On some Toeplitz matrices and their inversions, J. Egypt Math. Soc. 22 (2014), 420-423.
  • [11] R. Brawer, Potenzen der Pascal matrix und eine Identitat der Kombinatorik, Elem. der Math. 45 (1990), 107-110.
  • [12] A. Edelman and G. Strang, Pascal Matrices, The Mathematical Association of America, Monthly 111 (2004), 189-197.
  • [13] C. Lay David, Linear Algebra and Its Applications, 4th Ed. Boston, Pearson, Addison-Wesley, 2012.
  • [14] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, Cambridge, 1981.
  • [15] D.J.H. Garling, The α, β and γ Duality of Sequence Spaces, Proc. Comb. Phil. Soc. 63 (1967), 963-981.
  • [16] M. Stieglitz, H. Tietz, Matrixtransformationen von Folgenraumen Eine Ergebnis¨ubersict, Math. Z. 154 (1977), 1-16.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Harun Polat

Publication Date June 30, 2018
Submission Date March 27, 2018
Acceptance Date June 25, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

APA Polat, H. (2018). Some new Pascal sequence spaces. Fundamental Journal of Mathematics and Applications, 1(1), 61-68. https://doi.org/10.33401/fujma.409932
AMA Polat H. Some new Pascal sequence spaces. Fundam. J. Math. Appl. June 2018;1(1):61-68. doi:10.33401/fujma.409932
Chicago Polat, Harun. “Some New Pascal Sequence Spaces”. Fundamental Journal of Mathematics and Applications 1, no. 1 (June 2018): 61-68. https://doi.org/10.33401/fujma.409932.
EndNote Polat H (June 1, 2018) Some new Pascal sequence spaces. Fundamental Journal of Mathematics and Applications 1 1 61–68.
IEEE H. Polat, “Some new Pascal sequence spaces”, Fundam. J. Math. Appl., vol. 1, no. 1, pp. 61–68, 2018, doi: 10.33401/fujma.409932.
ISNAD Polat, Harun. “Some New Pascal Sequence Spaces”. Fundamental Journal of Mathematics and Applications 1/1 (June 2018), 61-68. https://doi.org/10.33401/fujma.409932.
JAMA Polat H. Some new Pascal sequence spaces. Fundam. J. Math. Appl. 2018;1:61–68.
MLA Polat, Harun. “Some New Pascal Sequence Spaces”. Fundamental Journal of Mathematics and Applications, vol. 1, no. 1, 2018, pp. 61-68, doi:10.33401/fujma.409932.
Vancouver Polat H. Some new Pascal sequence spaces. Fundam. J. Math. Appl. 2018;1(1):61-8.

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