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Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces

Year 2019, Volume: 2 Issue: 4, 293 - 302, 29.12.2019

Vakeel Ahmad Khan Sameera Aa Abdullah Kamal Mas Alshlool

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] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam-New York- Oxford, 1984.
  • [2] H. Nakano, Modulared sequence spaces, Proc. Japan Acad., 27(9) (1951), 508-512.
  • [3] S. Simons, The sequence spaces l(pv) and m(pv), Proc. Lond. Math. Soc., 3(1) (1965), 422-436.
  • [4] IJ. Maddox, Spaces of strongly summable sequences, Q. J. Math., 18(1) (1967), 345-355.
  • [5] IJ. Maddox, Paranormed sequence spaces generated by infinite matrices, Cambridge University Press, 64 (1968), 335-340.
  • [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] B. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4) (2009), 485-494.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • [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).
  • [11] Dems, Katarzyna, On I-Cauchy sequences, Real Anal. Exchange, 30(1) (2004), 123-128.
  • [12] K. Vakeel, A. Kamal, A. Sameera, Spaces of ideal convergent sequences of bounded linear operators, Numer. Funct. Anal. Optim., 39(12) (2018), 1278-1290.
  • [13] K. Vakeel, R. Rami, A. Kamal. A. Sameera, A. Ayaz, On ideal convergence Fibonacci difference sequence spaces, Adv. Difference Equ., 2018(1) (2018), 199.
  • [14] K. Vakeel, R. Rami, A. Kamal. A. Sameera, A. Esi, Some new spaces of ideal convergent double sequences by using compact operator, J. Appl. Sci., 17(9) (2017), 467-474.
  • [15] B. Tripathy, B. Hazarika, I-convergent sequence spaces associated with multiplier sequences, Math. Inequal. Appl., 11(3) (2008), 543.
  • [16] T. Salat, B. Tripathy, M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math, 17(5) (2005), 1-8.
  • [17] E. E. Kara, M. ˙Ilkhan, On some paranormed A-ideal convergent sequence spaces defined by Orlicz function, Asian J. Math. Comput. Research, 4(4) (2015), 183-194.
  • [18] M. Basarir, F. Basar, E. E. Kara, On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences, Sarajevo J. Math., 12(25) (2016), 2.
  • [19] M. Candan, K. Kayaduman , Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, Br. J. Math. Comput. Sci., 7(2) (2015), 150- 167.
  • [20] V. Karakaya, E. Savas, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Math. Slovaca, 63(4) (2013), 849-862.
  • [21] E. Malkowsky, Recent results in the theory of matrix transformations in sequence spaces, Mathmaticki Vesnik-Beograd, 49 (1997), 187-196.
  • [22] M.Mursaleen, On some new sequence spaces of non-absolute type related to the spaces `p and `¥ I, Filomat, 25(2) (2011), 33-51.
  • [23] K. Vakeel, A. Kamal, M. Abdullah, A. Sameera, On spaces of ideal convergent Fibonacci difference sequence defined by Orlicz function, Sigma, 37(1) (2019), 143-154.
  • [24] E. Kara, M. Demiriz, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes, 16(2) (2015), 907-923.
  • [25] H.Kizmaz, Certain sequence spaces, Can. Math. Bull, 24(2) (1981), 169-176.
  • [26] B.Tripathy, A. Esi, A new type of difference sequence spaces, Internat. J. Sci. Tech., 1(1) (2006), 11-14.
  • [27] S. Aydın, H. Polat, Difference sequence spaces derived by using Pascal transform, Fundam. J. Math. Appl., 2(1) (2019), 56-62.
  • [28] A. Esi, Some classes of generalized difference paranormed sequence spaces associated with multiplier sequences, J. Comput. Anal. Appl., 11(3) (2009).
  • [29] A. Esi, B. Tripathy, B. Sarma, On some new type generalized difference sequence spaces, Math. Slovaca, 57(5) (2007), 475-482.
  • [30] E. E. Kara, M. ˙Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208-2223.
  • [31] T. Salat, M. Tripathy, M. Ziman, On some properties of i-convergence, Tatra Mt. Math. Publ, 28(5) (2004), 279-289.
  • [32] C. Lascarides, On the equivalence of certain sets of sequences, Indian J. Math., 25(1) (1983), 41-52.
  • [33] G. Petersen, Regular Matrix Transformations, McGraw-Hill, 1966.

Year 2019, Volume: 2 Issue: 4, 293 - 302, 29.12.2019

Vakeel Ahmad Khan Sameera Aa Abdullah Kamal Mas Alshlool

Abstract

Project Number

amu231678

References

  • [1] A. Wilansky, Summability Through Functional Analysis, North-Holland Mathematics Studies, Amsterdam-New York- Oxford, 1984.
  • [2] H. Nakano, Modulared sequence spaces, Proc. Japan Acad., 27(9) (1951), 508-512.
  • [3] S. Simons, The sequence spaces l(pv) and m(pv), Proc. Lond. Math. Soc., 3(1) (1965), 422-436.
  • [4] IJ. Maddox, Spaces of strongly summable sequences, Q. J. Math., 18(1) (1967), 345-355.
  • [5] IJ. Maddox, Paranormed sequence spaces generated by infinite matrices, Cambridge University Press, 64 (1968), 335-340.
  • [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] B. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4) (2009), 485-494.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  • [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).
  • [11] Dems, Katarzyna, On I-Cauchy sequences, Real Anal. Exchange, 30(1) (2004), 123-128.
  • [12] K. Vakeel, A. Kamal, A. Sameera, Spaces of ideal convergent sequences of bounded linear operators, Numer. Funct. Anal. Optim., 39(12) (2018), 1278-1290.
  • [13] K. Vakeel, R. Rami, A. Kamal. A. Sameera, A. Ayaz, On ideal convergence Fibonacci difference sequence spaces, Adv. Difference Equ., 2018(1) (2018), 199.
  • [14] K. Vakeel, R. Rami, A. Kamal. A. Sameera, A. Esi, Some new spaces of ideal convergent double sequences by using compact operator, J. Appl. Sci., 17(9) (2017), 467-474.
  • [15] B. Tripathy, B. Hazarika, I-convergent sequence spaces associated with multiplier sequences, Math. Inequal. Appl., 11(3) (2008), 543.
  • [16] T. Salat, B. Tripathy, M. Ziman, On I-convergence field, Ital. J. Pure Appl. Math, 17(5) (2005), 1-8.
  • [17] E. E. Kara, M. ˙Ilkhan, On some paranormed A-ideal convergent sequence spaces defined by Orlicz function, Asian J. Math. Comput. Research, 4(4) (2015), 183-194.
  • [18] M. Basarir, F. Basar, E. E. Kara, On the spaces of Fibonacci difference absolutely p-summable, null and convergent sequences, Sarajevo J. Math., 12(25) (2016), 2.
  • [19] M. Candan, K. Kayaduman , Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, Br. J. Math. Comput. Sci., 7(2) (2015), 150- 167.
  • [20] V. Karakaya, E. Savas, H. Polat, Some paranormed Euler sequence spaces of difference sequences of order m, Math. Slovaca, 63(4) (2013), 849-862.
  • [21] E. Malkowsky, Recent results in the theory of matrix transformations in sequence spaces, Mathmaticki Vesnik-Beograd, 49 (1997), 187-196.
  • [22] M.Mursaleen, On some new sequence spaces of non-absolute type related to the spaces `p and `¥ I, Filomat, 25(2) (2011), 33-51.
  • [23] K. Vakeel, A. Kamal, M. Abdullah, A. Sameera, On spaces of ideal convergent Fibonacci difference sequence defined by Orlicz function, Sigma, 37(1) (2019), 143-154.
  • [24] E. Kara, M. Demiriz, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes, 16(2) (2015), 907-923.
  • [25] H.Kizmaz, Certain sequence spaces, Can. Math. Bull, 24(2) (1981), 169-176.
  • [26] B.Tripathy, A. Esi, A new type of difference sequence spaces, Internat. J. Sci. Tech., 1(1) (2006), 11-14.
  • [27] S. Aydın, H. Polat, Difference sequence spaces derived by using Pascal transform, Fundam. J. Math. Appl., 2(1) (2019), 56-62.
  • [28] A. Esi, Some classes of generalized difference paranormed sequence spaces associated with multiplier sequences, J. Comput. Anal. Appl., 11(3) (2009).
  • [29] A. Esi, B. Tripathy, B. Sarma, On some new type generalized difference sequence spaces, Math. Slovaca, 57(5) (2007), 475-482.
  • [30] E. E. Kara, M. ˙Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra, 64(11) (2016), 2208-2223.
  • [31] T. Salat, M. Tripathy, M. Ziman, On some properties of i-convergence, Tatra Mt. Math. Publ, 28(5) (2004), 279-289.
  • [32] C. Lascarides, On the equivalence of certain sets of sequences, Indian J. Math., 25(1) (1983), 41-52.
  • [33] G. Petersen, Regular Matrix Transformations, McGraw-Hill, 1966.
There are 32 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Vakeel Ahmad Khan 0000-0002-4132-0954

Sameera Aa Abdullah This is me 0000-0003-0029-2405

Kamal Mas Alshlool This is me 0000-0003-0029-2405

Project Number amu231678
Publication Date December 29, 2019
Submission Date July 24, 2019
Acceptance Date October 1, 2019
Published in Issue Year 2019 Volume: 2 Issue: 4

Cite

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.
AMA Khan VA, Abdullah SA, Alshlool KM. Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences. December 2019;2(4):293-302.
Chicago Khan, Vakeel Ahmad, Sameera Aa Abdullah, and Kamal Mas Alshlool. “Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces”. Communications in Advanced Mathematical Sciences 2, no. 4 (December 2019): 293-302.
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 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, 2019.
ISNAD Khan, Vakeel Ahmad et al. “Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces”. Communications in Advanced Mathematical Sciences 2/4 (December 2019), 293-302.
JAMA 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, 2019, pp. 293-02.
Vancouver Khan VA, Abdullah SA, Alshlool KM. Paranorm Ideal Convergent Fibonacci Difference Sequence Spaces. Communications in Advanced Mathematical Sciences. 2019;2(4):293-302.
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