Research Article

Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces

Volume: 2 Number: 4 December 29, 2019
Vakeel Ahmad Khan *, Sameera Aa Abdullah , Kamal Mas Alshlool
EN

Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces

Abstract

In this paper  we  introduce some new sequence spaces $ c_{0}^{I}(\hat{F},p)$, $c^{I}(\hat{F},p)$ and $\ell_{\infty}^{I}(\hat{F},p)$ for  $p=(p_n),$ a sequence of positive real numbers. In addition, we study  some topological and algebraic properties on these spaces. Lastly, we  examine  some inclusion relations on these spaces.

Keywords

Fibonacci difference matrix,I-Cauchy,I-convergence,Paranormed space

Supporting Institution

aligarh muslim university aligarh india

Project Number

amu231678

References

  1. [1] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam-New York- Oxford, 1984.
  2. [2] H. Nakano, Modulared sequence spaces, Proc. Japan Acad., 27(9) (1951), 508-512.
  3. [3] S. Simons, The sequence spaces l(pv) and m(pv), Proc. Lond. Math. Soc., 3(1) (1965), 422-436.
  4. [4] IJ. Maddox, Spaces of strongly summable sequences, Q. J. Math., 18(1) (1967), 345-355.
  5. [5] IJ. Maddox, Paranormed sequence spaces generated by infinite matrices, Cambridge University Press, 64 (1968), 335-340.
  6. [6] H. Ellidokuzo˘glu, S. Demiriz, A. K¨oseo˘glu On the paranormed binomial sequence spaces, Univers. J. Math. Appl., 1(3) (2018), 137-147.
  7. [7] B. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4) (2009), 485-494.
  8. [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  9. [9] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73-74. [10] P. Kostyrko, M. Macaj, T.Salat, Statistical convergence and I–convergence, Real Anal. Exchange, (1999).
  10. [11] Dems, Katarzyna, On I-Cauchy sequences, Real Anal. Exchange, 30(1) (2004), 123-128.
APA
Khan, V. A., Abdullah, S. A., & Alshlool, K. M. (2019). Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences, 2(4), 293-302. https://izlik.org/JA73PU55ZK
AMA
1.Khan VA, Abdullah SA, Alshlool KM. Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences. 2019;2(4):293-302. https://izlik.org/JA73PU55ZK
Chicago
Khan, Vakeel Ahmad, Sameera Aa Abdullah, and Kamal Mas Alshlool. 2019. “Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces”. Communications in Advanced Mathematical Sciences 2 (4): 293-302. https://izlik.org/JA73PU55ZK.
EndNote
Khan VA, Abdullah SA, Alshlool KM (December 1, 2019) Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences 2 4 293–302.
IEEE
[1]V. A. Khan, S. A. Abdullah, and K. M. Alshlool, “Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces”, Communications in Advanced Mathematical Sciences, vol. 2, no. 4, pp. 293–302, Dec. 2019, [Online]. Available: https://izlik.org/JA73PU55ZK
ISNAD
Khan, Vakeel Ahmad - Abdullah, Sameera Aa - Alshlool, Kamal Mas. “Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces”. Communications in Advanced Mathematical Sciences 2/4 (December 1, 2019): 293-302. https://izlik.org/JA73PU55ZK.
JAMA
1.Khan VA, Abdullah SA, Alshlool KM. Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences. 2019;2:293–302.
MLA
Khan, Vakeel Ahmad, et al. “Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces”. Communications in Advanced Mathematical Sciences, vol. 2, no. 4, Dec. 2019, pp. 293-02, https://izlik.org/JA73PU55ZK.
Vancouver
1.Vakeel Ahmad Khan, Sameera Aa Abdullah, Kamal Mas Alshlool. Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences [Internet]. 2019 Dec. 1;2(4):293-302. Available from: https://izlik.org/JA73PU55ZK