Conference Paper
BibTex RIS Cite

Year 2019, Volume: 2 Issue: 3, 194 - 197, 30.12.2019

Mikail Et Rifat Colak

Abstract

References

  • [1] W. L. C. Sargent, Some sequence spacess related to $\ell_{p}$ spaces, J. London Math. Soc. 35 (1960), 161-171.
  • [2] B. C. Tripathy, M. Sen, On a new class of sequences related to the space $\ell_{p},$; Tamkang J. Math. 33(2) (2002), 167-171.
  • [3] B. C. Tripathy, S. Mahanta, On a class of sequences related to the $\ell_{p}$ space defined by Orlicz functions, Soochow J. Math. 29(4) (2003), 379–391.
  • [4] H. Kızmaz, On certain Sequence spaces, Canad. Math. Bull. 24(2) (1981), 169-176.
  • [5] M. Et, R. Çolak, On generalized difference sequence spaces, Soochow J. Math. 21(4) (1995), 377-386.
  • [6] A. Esi, B. C. Tripathy, B. Sarma, On some new type generalized difference sequence spaces, Math. Slovaca 57(5) (2007), 475–482.
  • [7] A. Esi, B. C. Tripathy, A New Type Of Difference Sequence Spaces, International Journal of Science & Technology 1(1) (2006), 11-14.
  • [8] B . C. Tripathy, A. Esi, B. K. Tripathy, On a new type of generalized difference Cesaro Sequence spaces, Soochow J. Math. 31(3) (2005), 333-340.
  • [9] Y. Altin, Properties of some sets of sequences defined by a modulus function, Acta Math. Sci. Ser. B Engl. Ed. 29(2) (2009), 427–434.
  • [10] H. Altinok, M. Et, R. Çolak, Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers, Iran. J. Fuzzy Syst. 11(5) (2014), 39–46, 109.
  • [11] S. Demiriz, C. Çakan, Some topological and geometrical properties of a new difference sequence space. Abstr. Appl. Anal. 2011, Art. ID 213878, 14 pp.
  • [12] S. Erdem, S. Demiriz, On the new generalized block difference sequence spaces, Appl. Appl. Math., Special Issue No. 5 (2019), 68–83.
  • [13] M. Et, A. Alotaibi, S. A. Mohiuddine, On $(\Delta^{m},I)$-statistical convergence of order $\alpha,$, The Scientific World Journal, 2014, 535419 DOI: 10.1155/2014/535419.
  • [14] M. Et, M. Mursaleen, M. Işık, On a class of fuzzy sets defined by Orlicz functions, Filomat 27(5) (2013), 789–796.
  • [15] M. Et, V. Karakaya, A new difference sequence set of order Alpha and its geometrical properties, Abstr. Appl. Anal. 2014, Art. ID 278907, 4 pp.
  • [16] M. Karaka¸s, M. Et, V. Karakaya, Some geometric properties of a new difference sequence space involving lacunary sequences, Acta Math. Sci. Ser. B (Engl. Ed.) 33(6) (2013), 1711–1720.
  • [17] M. A. Sarıgöl, On difference sequence spaces, J. Karadeniz Tech. Univ. Fac. Arts Sci. Ser. Math.-Phys. 10 (1987), 63–71.
  • [18] E. Sava¸s, M. Et, On $(\Delta_{\lambda}^{m},I)-$statistical convergence of order $\alpha$, Period. Math. Hungar. 71(2) (2015), 135–145.
  • [19] R. Çolak, M. Et, On some difference sequence sets and their topological properties, Bull. Malays. Math. Sci. Soc. 28(2) (2005), 125–130.

A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $

Year 2019, Volume: 2 Issue: 3, 194 - 197, 30.12.2019

Mikail Et Rifat Colak

Abstract

Let $\left( \phi_{n}\right) $ be a non-decreasing sequence of positive numbers such that $n\phi_{n+1}\leq \left( n+1\right) \phi_{n}$ for all $n\in \mathbb{N}$. The class of all sequences $\left( \phi_{n}\right) $ is denoted by $\Phi$. The sequence space $m\left( \phi \right) $ was introduced by Sargent [1] and he studied some of its properties and obtained some relations with the space $\ell_{p}$. Later on it was investigated by Tripathy and Sen [2] and Tripathy and Mahanta [3]. In this work, using the generalized difference operator $\Delta_{m}^{n}$, we generalize the sequence space $m\left( \phi \right) $ to sequence space $ m\left( \phi,p\right) \left( \Delta _{m}^{n}\right) ,$ give some topological properties about this space and show that the space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $ is a $BK-$space by a suitable norm$.$ The results obtained are generalizes some known results.

Keywords

Difference sequence BK-space Symmetric space Normal space.

References

  • [1] W. L. C. Sargent, Some sequence spacess related to $\ell_{p}$ spaces, J. London Math. Soc. 35 (1960), 161-171.
  • [2] B. C. Tripathy, M. Sen, On a new class of sequences related to the space $\ell_{p},$; Tamkang J. Math. 33(2) (2002), 167-171.
  • [3] B. C. Tripathy, S. Mahanta, On a class of sequences related to the $\ell_{p}$ space defined by Orlicz functions, Soochow J. Math. 29(4) (2003), 379–391.
  • [4] H. Kızmaz, On certain Sequence spaces, Canad. Math. Bull. 24(2) (1981), 169-176.
  • [5] M. Et, R. Çolak, On generalized difference sequence spaces, Soochow J. Math. 21(4) (1995), 377-386.
  • [6] A. Esi, B. C. Tripathy, B. Sarma, On some new type generalized difference sequence spaces, Math. Slovaca 57(5) (2007), 475–482.
  • [7] A. Esi, B. C. Tripathy, A New Type Of Difference Sequence Spaces, International Journal of Science & Technology 1(1) (2006), 11-14.
  • [8] B . C. Tripathy, A. Esi, B. K. Tripathy, On a new type of generalized difference Cesaro Sequence spaces, Soochow J. Math. 31(3) (2005), 333-340.
  • [9] Y. Altin, Properties of some sets of sequences defined by a modulus function, Acta Math. Sci. Ser. B Engl. Ed. 29(2) (2009), 427–434.
  • [10] H. Altinok, M. Et, R. Çolak, Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers, Iran. J. Fuzzy Syst. 11(5) (2014), 39–46, 109.
  • [11] S. Demiriz, C. Çakan, Some topological and geometrical properties of a new difference sequence space. Abstr. Appl. Anal. 2011, Art. ID 213878, 14 pp.
  • [12] S. Erdem, S. Demiriz, On the new generalized block difference sequence spaces, Appl. Appl. Math., Special Issue No. 5 (2019), 68–83.
  • [13] M. Et, A. Alotaibi, S. A. Mohiuddine, On $(\Delta^{m},I)$-statistical convergence of order $\alpha,$, The Scientific World Journal, 2014, 535419 DOI: 10.1155/2014/535419.
  • [14] M. Et, M. Mursaleen, M. Işık, On a class of fuzzy sets defined by Orlicz functions, Filomat 27(5) (2013), 789–796.
  • [15] M. Et, V. Karakaya, A new difference sequence set of order Alpha and its geometrical properties, Abstr. Appl. Anal. 2014, Art. ID 278907, 4 pp.
  • [16] M. Karaka¸s, M. Et, V. Karakaya, Some geometric properties of a new difference sequence space involving lacunary sequences, Acta Math. Sci. Ser. B (Engl. Ed.) 33(6) (2013), 1711–1720.
  • [17] M. A. Sarıgöl, On difference sequence spaces, J. Karadeniz Tech. Univ. Fac. Arts Sci. Ser. Math.-Phys. 10 (1987), 63–71.
  • [18] E. Sava¸s, M. Et, On $(\Delta_{\lambda}^{m},I)-$statistical convergence of order $\alpha$, Period. Math. Hungar. 71(2) (2015), 135–145.
  • [19] R. Çolak, M. Et, On some difference sequence sets and their topological properties, Bull. Malays. Math. Sci. Soc. 28(2) (2005), 125–130.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mikail Et 0000-0001-8292-7819

Rifat Colak 0000-0001-8161-5186

Publication Date December 30, 2019
Acceptance Date December 12, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Et, M., & Colak, R. (2019). A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $. Conference Proceedings of Science and Technology, 2(3), 194-197.
AMA Et M, Colak R. A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $. Conference Proceedings of Science and Technology. December 2019;2(3):194-197.
Chicago Et, Mikail, and Rifat Colak. “A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 194-97.
EndNote Et M, Colak R (December 1, 2019) A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $. Conference Proceedings of Science and Technology 2 3 194–197.
IEEE M. Et and R. Colak, “A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 194–197, 2019.
ISNAD Et, Mikail - Colak, Rifat. “A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $”. Conference Proceedings of Science and Technology 2/3 (December 2019), 194-197.
JAMA Et M, Colak R. A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $. Conference Proceedings of Science and Technology. 2019;2:194–197.
MLA Et, Mikail and Rifat Colak. “A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 194-7.
Vancouver Et M, Colak R. A New Type Generalized Difference Sequence Space $m\left( \phi,p\right) \left( \Delta_{m}^{n}\right) $. Conference Proceedings of Science and Technology. 2019;2(3):194-7.
 Download Cover Image