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Year 2018, , 137 - 147, 30.09.2018
https://doi.org/10.32323/ujma.395247

Abstract

References

  • [1] B. Altay, F. Başar, On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math., 26, 701-715 (2002).
  • [2] B. Altay, F. Başar, Some paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math., 30, 591-608 (2006).
  • [3] F. Başar, B. Altay, Matrix mappings on the space bs(p) and its a−,b− and g−duals, Aligarh Bull. Math., 21(1), 79-91 (2002).
  • [4] F. Başar, Infinite matrices and almost boundedness, Boll. Un. Mat. Ital., 6(7), 395-402 (1992).
  • [5] M. C. Bişgin, The binomial sequence spaces of nonabsolute type, J. Inequal. Appl. 309 (2016).
  • [6] M. C. Bişgin, The binomial sequence spaces which include the spaces ℓp and ℓ¥ and geometric properties, J. Inequal. Appl. 304 (2016).
  • [7] B. Choudhary, S. K. Mishra, On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations, Indian J. Pure Appl. Math., 24(5), 291-301 (1993).
  • [8] S. Demiriz, C. C¸ akan, On Some New Paranormed Euler Sequence Spaces and Euler Core, Acta Math. Sin.(Eng. Ser.), 26(7), 1207-1222 (2010).
  • [9] S. Demiriz, H. B. Ellidokuzoğlu, On The Paranormed Taylor Sequence Spaces, Konuralp Journal Of Mathematics, 4(2), 132-148 (2016).
  • [10] K. G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox. J. Math. Anal. Appl., 180, 223-238 (1993).
  • [11] A. Jarrah and E. Malkowsky, BK spaces, bases and linear operators, Rend. Circ. Mat. Palermo, 52(2), 177-191 (1990).
  • [12] E. E. Kara and M. lkhan, On some Banach sequence spaces derived by a new band matrix, Br. J. Math. Comput. Sci., 9(2), 141-159 (2015). [13] E. E. Kara and M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11), 2208-2223 (2016). [14] M. Kirişci, On the Taylor sequence spaces of nonabsulate type which include the spaces c0 and c, J. Math. Anal., 6(2), 22-35 (2015).
  • [15] M. Kirişci, The application domain of infinite matrices with algorithms, Univ. J. Math. Appl., 1(1), 1-9 (2018).
  • [16] M. Candan and A. Güneş, Paranormed sequence space of non-absolute type founded using generalized difference matrix, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85(2), 269-276 (2015).
  • [17] C. G. Lascarides and I. J. Maddox, Matrix transformations between some classes of sequences, Proc.Camb. Phil. Soc., 68, 99-104 (1970).
  • [18] I.J. Maddox, Elements of Functional Analysis, second ed., The University Press, Cambridge, 1988.
  • [19] I. J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phios. Soc., 64, 335-340 (1968).
  • [20] H. Nakano, Modulared sequence spaces, Proc. Jpn. Acad., 27(2), 508-512 (1951).
  • [21] S. Simons, The sequence spaces ℓ(pv) and m(pv). Proc. London Math. Soc., 15(3), 422-436 (1965).

On the paranormed binomial sequence spaces

Year 2018, , 137 - 147, 30.09.2018
https://doi.org/10.32323/ujma.395247

Abstract

In this paper the sequence spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ are linearly isomorphic to spaces $c_0(p)$, $c(p)$, $\ell_{\infty}(p)$ and $\ell(p)$, respectively. Besides this, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, and $b^{r,s}(p)$ have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices $(b_0^{r,s}(p) : \mu)$, $(b^{r,s}_c(p): \mu)$ and $(b^{r,s}(p): \mu)$ have been characterized, where $\mu$ is one of the sequence spaces $\ell_\infty,c$ and $c_0$ and derives the other characterizations for the special cases of $\mu$.

References

  • [1] B. Altay, F. Başar, On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math., 26, 701-715 (2002).
  • [2] B. Altay, F. Başar, Some paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math., 30, 591-608 (2006).
  • [3] F. Başar, B. Altay, Matrix mappings on the space bs(p) and its a−,b− and g−duals, Aligarh Bull. Math., 21(1), 79-91 (2002).
  • [4] F. Başar, Infinite matrices and almost boundedness, Boll. Un. Mat. Ital., 6(7), 395-402 (1992).
  • [5] M. C. Bişgin, The binomial sequence spaces of nonabsolute type, J. Inequal. Appl. 309 (2016).
  • [6] M. C. Bişgin, The binomial sequence spaces which include the spaces ℓp and ℓ¥ and geometric properties, J. Inequal. Appl. 304 (2016).
  • [7] B. Choudhary, S. K. Mishra, On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations, Indian J. Pure Appl. Math., 24(5), 291-301 (1993).
  • [8] S. Demiriz, C. C¸ akan, On Some New Paranormed Euler Sequence Spaces and Euler Core, Acta Math. Sin.(Eng. Ser.), 26(7), 1207-1222 (2010).
  • [9] S. Demiriz, H. B. Ellidokuzoğlu, On The Paranormed Taylor Sequence Spaces, Konuralp Journal Of Mathematics, 4(2), 132-148 (2016).
  • [10] K. G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox. J. Math. Anal. Appl., 180, 223-238 (1993).
  • [11] A. Jarrah and E. Malkowsky, BK spaces, bases and linear operators, Rend. Circ. Mat. Palermo, 52(2), 177-191 (1990).
  • [12] E. E. Kara and M. lkhan, On some Banach sequence spaces derived by a new band matrix, Br. J. Math. Comput. Sci., 9(2), 141-159 (2015). [13] E. E. Kara and M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11), 2208-2223 (2016). [14] M. Kirişci, On the Taylor sequence spaces of nonabsulate type which include the spaces c0 and c, J. Math. Anal., 6(2), 22-35 (2015).
  • [15] M. Kirişci, The application domain of infinite matrices with algorithms, Univ. J. Math. Appl., 1(1), 1-9 (2018).
  • [16] M. Candan and A. Güneş, Paranormed sequence space of non-absolute type founded using generalized difference matrix, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85(2), 269-276 (2015).
  • [17] C. G. Lascarides and I. J. Maddox, Matrix transformations between some classes of sequences, Proc.Camb. Phil. Soc., 68, 99-104 (1970).
  • [18] I.J. Maddox, Elements of Functional Analysis, second ed., The University Press, Cambridge, 1988.
  • [19] I. J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phios. Soc., 64, 335-340 (1968).
  • [20] H. Nakano, Modulared sequence spaces, Proc. Jpn. Acad., 27(2), 508-512 (1951).
  • [21] S. Simons, The sequence spaces ℓ(pv) and m(pv). Proc. London Math. Soc., 15(3), 422-436 (1965).
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Hacer Bilgin Ellidokuzoğlu

Serkan Demiriz

Ali Köseoğlu

Publication Date September 30, 2018
Submission Date February 15, 2018
Acceptance Date March 6, 2018
Published in Issue Year 2018

Cite

APA Bilgin Ellidokuzoğlu, H., Demiriz, S., & Köseoğlu, A. (2018). On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications, 1(3), 137-147. https://doi.org/10.32323/ujma.395247
AMA Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A. On the paranormed binomial sequence spaces. Univ. J. Math. Appl. September 2018;1(3):137-147. doi:10.32323/ujma.395247
Chicago Bilgin Ellidokuzoğlu, Hacer, Serkan Demiriz, and Ali Köseoğlu. “On the Paranormed Binomial Sequence Spaces”. Universal Journal of Mathematics and Applications 1, no. 3 (September 2018): 137-47. https://doi.org/10.32323/ujma.395247.
EndNote Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A (September 1, 2018) On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications 1 3 137–147.
IEEE H. Bilgin Ellidokuzoğlu, S. Demiriz, and A. Köseoğlu, “On the paranormed binomial sequence spaces”, Univ. J. Math. Appl., vol. 1, no. 3, pp. 137–147, 2018, doi: 10.32323/ujma.395247.
ISNAD Bilgin Ellidokuzoğlu, Hacer et al. “On the Paranormed Binomial Sequence Spaces”. Universal Journal of Mathematics and Applications 1/3 (September 2018), 137-147. https://doi.org/10.32323/ujma.395247.
JAMA Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A. On the paranormed binomial sequence spaces. Univ. J. Math. Appl. 2018;1:137–147.
MLA Bilgin Ellidokuzoğlu, Hacer et al. “On the Paranormed Binomial Sequence Spaces”. Universal Journal of Mathematics and Applications, vol. 1, no. 3, 2018, pp. 137-4, doi:10.32323/ujma.395247.
Vancouver Bilgin Ellidokuzoğlu H, Demiriz S, Köseoğlu A. On the paranormed binomial sequence spaces. Univ. J. Math. Appl. 2018;1(3):137-4.

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