Research Article
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Year 2020, , 76 - 81, 12.11.2020
https://doi.org/10.47087/mjm.733096

Abstract

References

  • [1] P. Das, E. Savas, S. K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters, 24 (2011), 1509 - 1514.
  • [2] S. Gahler, 2-metrische Raume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115 -148.
  • [3] H. Gunawan and Mashadi, On Finite Dimensional 2-normed spaces, Soochow J. Math., 27(3) (2001), 321 - 329.
  • [4] I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc., 100 (1986), 161-166.
  • [5] P. Kostyrko, M. Macaj and T. Salat, I-Convergence, Real Anal. Exchange, 26 (2) (2000), 669- 686.
  • [6] P. Kostyrko, M. Macaj, T. Salat and M. Sleziak, I-Convergence and Extremal I-Limit Points, Math. Slovaca, 55(2005), 443-464.
  • [7] M. A. Krasnoselskii and Y. B. Rutisky, Convex function and Orlicz spaces, Groningen, Netherlands, 1961.
  • [8] Mursaleen, Q.A. Khan, , and T. A. Chishti, Some new Convergent sequences spaces defined by Orlicz Functions and Statistical convergence, Ital. J. Pure Appl. Math., 9 (2001), 25-32.
  • [9] S.D. Parashar, and B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure appl. Math., 25(4) (1994), 419-428.
  • [10] W. Raymond, Y. Freese and J. Cho, Geometry of linear 2-normed spaces, N.Y. Nova Science Publishers, Huntington, 2001.
  • [11] W. H. Ruckle, FK Spaces in which the sequence of coordinate vectors in bounded, Cand, J. Math. 25 (1973) 973-978.
  • [12] A. Sahiner, M. Gurdal, S. Saltan and H. Gunawan, Ideal Convergence in 2-normed spaces, Taiwanese Journal of Mathematics, 11(5) 2007; 1477 -1484.
  • [13] E. Savas, Pratulananda Das, A generalized statistical convergence via ideals, Appl. Math. Letters, 24 (2011), 826 - 830.
  • [14] E. Savas, Pratulananda Das, S. Dutta, A note on strong matrix summability via ideals, Appl. Math Letters, 25 (4) (2012), 733 - 738.
  • [15] E. Savas, R.F. Patterson ; (lambda; sigma)-double sequence spaces via Orlicz function, J. Comput. Anal. App., 10(1), (2008),101-111.
  • [16] E. Savas, and R. F. Patterson, Some sigma-Double Sequence Spaces Defined by Orlicz Function, J. Math. Anal. Appl. 324 (2006), no. 1, 525-531.
  • [17] E. Savas, and R. Savas, Some λ-sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math. 34(12) (2003), 1673-1680.
  • [18] E.Savas, Some new double sequence spaces defined by Orlicz function in n-normed space. J. Inequal. Appl. 2011, Art. ID 592840, 9 pp.
  • [19] E. Savas , On Some New Sequence Spaces in 2-Normed Spaces Using Ideal Convergence and an Orlicz Function, J.Ineq. Appl. Vol. 2010 (2010), Article ID 482392, 1-8.
  • [20] E. Savas , m -strongly summable sequences spaces in 2-Normed Spaces defined by Ideal Convergence and an Orlicz Function, App. Math. Comp., 217(2010), 271-276.

\mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces

Year 2020, , 76 - 81, 12.11.2020
https://doi.org/10.47087/mjm.733096

Abstract

One of the wide-ranging applications and research areas of Summability theory is the concept of statistical convergence. This concept was studied a related concept of convergence by using lacunary sequence by Fridy and Orhan. At the last quarter of the 20th century, lacunary statistical convergence has been discussed and captured significant aspect of creating the basis of several investigations conducted in many branches of mathematics. On the other hand, in 1961 Krasnoselskii and Rutisky presented the definition of Orlicz function. Also, in 1963 G\"{a}hler introduced the notion of 2-normed spaces. The main goal of this article is to introduce $\mathcal{I}-$ almost convergence of lacunary sequences with regard to an Orlicz function
in 2-normed spaces and other sequence spaces by considering the concept of
ideal that was presented by Kostyrko and others. Additionally, we examine the relationship between these sequence spaces and fundamental inclusion theorems are investigated.

References

  • [1] P. Das, E. Savas, S. K. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters, 24 (2011), 1509 - 1514.
  • [2] S. Gahler, 2-metrische Raume und ihre topologische Struktur, Math. Nachr., 26 (1963), 115 -148.
  • [3] H. Gunawan and Mashadi, On Finite Dimensional 2-normed spaces, Soochow J. Math., 27(3) (2001), 321 - 329.
  • [4] I.J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc., 100 (1986), 161-166.
  • [5] P. Kostyrko, M. Macaj and T. Salat, I-Convergence, Real Anal. Exchange, 26 (2) (2000), 669- 686.
  • [6] P. Kostyrko, M. Macaj, T. Salat and M. Sleziak, I-Convergence and Extremal I-Limit Points, Math. Slovaca, 55(2005), 443-464.
  • [7] M. A. Krasnoselskii and Y. B. Rutisky, Convex function and Orlicz spaces, Groningen, Netherlands, 1961.
  • [8] Mursaleen, Q.A. Khan, , and T. A. Chishti, Some new Convergent sequences spaces defined by Orlicz Functions and Statistical convergence, Ital. J. Pure Appl. Math., 9 (2001), 25-32.
  • [9] S.D. Parashar, and B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure appl. Math., 25(4) (1994), 419-428.
  • [10] W. Raymond, Y. Freese and J. Cho, Geometry of linear 2-normed spaces, N.Y. Nova Science Publishers, Huntington, 2001.
  • [11] W. H. Ruckle, FK Spaces in which the sequence of coordinate vectors in bounded, Cand, J. Math. 25 (1973) 973-978.
  • [12] A. Sahiner, M. Gurdal, S. Saltan and H. Gunawan, Ideal Convergence in 2-normed spaces, Taiwanese Journal of Mathematics, 11(5) 2007; 1477 -1484.
  • [13] E. Savas, Pratulananda Das, A generalized statistical convergence via ideals, Appl. Math. Letters, 24 (2011), 826 - 830.
  • [14] E. Savas, Pratulananda Das, S. Dutta, A note on strong matrix summability via ideals, Appl. Math Letters, 25 (4) (2012), 733 - 738.
  • [15] E. Savas, R.F. Patterson ; (lambda; sigma)-double sequence spaces via Orlicz function, J. Comput. Anal. App., 10(1), (2008),101-111.
  • [16] E. Savas, and R. F. Patterson, Some sigma-Double Sequence Spaces Defined by Orlicz Function, J. Math. Anal. Appl. 324 (2006), no. 1, 525-531.
  • [17] E. Savas, and R. Savas, Some λ-sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math. 34(12) (2003), 1673-1680.
  • [18] E.Savas, Some new double sequence spaces defined by Orlicz function in n-normed space. J. Inequal. Appl. 2011, Art. ID 592840, 9 pp.
  • [19] E. Savas , On Some New Sequence Spaces in 2-Normed Spaces Using Ideal Convergence and an Orlicz Function, J.Ineq. Appl. Vol. 2010 (2010), Article ID 482392, 1-8.
  • [20] E. Savas , m -strongly summable sequences spaces in 2-Normed Spaces defined by Ideal Convergence and an Orlicz Function, App. Math. Comp., 217(2010), 271-276.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Rabia Savas

Publication Date November 12, 2020
Acceptance Date November 5, 2020
Published in Issue Year 2020

Cite

APA Savas, R. (2020). \mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces. Maltepe Journal of Mathematics, 2(2), 76-81. https://doi.org/10.47087/mjm.733096
AMA Savas R. \mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces. Maltepe Journal of Mathematics. November 2020;2(2):76-81. doi:10.47087/mjm.733096
Chicago Savas, Rabia. “\mathcal{I}- Almost Lacunary Vector Valued Sequence Spaces in 2- Normed Spaces”. Maltepe Journal of Mathematics 2, no. 2 (November 2020): 76-81. https://doi.org/10.47087/mjm.733096.
EndNote Savas R (November 1, 2020) \mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces. Maltepe Journal of Mathematics 2 2 76–81.
IEEE R. Savas, “\mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces”, Maltepe Journal of Mathematics, vol. 2, no. 2, pp. 76–81, 2020, doi: 10.47087/mjm.733096.
ISNAD Savas, Rabia. “\mathcal{I}- Almost Lacunary Vector Valued Sequence Spaces in 2- Normed Spaces”. Maltepe Journal of Mathematics 2/2 (November 2020), 76-81. https://doi.org/10.47087/mjm.733096.
JAMA Savas R. \mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces. Maltepe Journal of Mathematics. 2020;2:76–81.
MLA Savas, Rabia. “\mathcal{I}- Almost Lacunary Vector Valued Sequence Spaces in 2- Normed Spaces”. Maltepe Journal of Mathematics, vol. 2, no. 2, 2020, pp. 76-81, doi:10.47087/mjm.733096.
Vancouver Savas R. \mathcal{I}- almost Lacunary vector valued sequence spaces in 2- normed spaces. Maltepe Journal of Mathematics. 2020;2(2):76-81.

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