호남수학학술지 (Honam Mathematical Journal)

  • 제41권4호
  • /
  • Pages.757-768
  • /
  • 2019
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ROUGH TRIPLE SEQUENCES IN GRADUAL NORMED SPACES

  • 투고 : 2019.02.09
  • 심사 : 2019.06.27
  • 발행 : 2019.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we investigate general topological properties of rough triple sequences in a gradual normed space. We define some new notions such as rough gradual convergent of triple sequences, rough triple gradual Cauchy sequences, etc.

키워드

참고문헌

  1. S. Aytar, Rough statistical convergence, Numer. Funct. Anal. Optim., 29(3-4) (2008), 291-303. https://doi.org/10.1080/01630560802001064
  2. S. Aytar, The rough limit set and the core of a real sequence, Numer. Funct. Anal. Optim., 29(3-4) (2008), 283-290. https://doi.org/10.1080/01630560802001056
  3. A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures, 1(2) (2014), 16-25.
  4. A. Esi and M. N. Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis, 2(1) (2014), 6-10.
  5. A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9(5) (2015), 2529-2534.
  6. A. Esi, S. Araci and M. Acikgoz, Statistical convergence of Bernstein operators, Appl. Math. Inf. Sci., 10(6) (2016), 2083-2086. https://doi.org/10.18576/amis/100610
  7. A. Esi, S. Araci and A. Esi, ${\lambda}$-Statistical convergence of Bernstein polynomial sequences, Advances and Applications in Mathematical Sciences, 16(3) (2017), 113-119.
  8. A. Esi, N. Subramanian and A. Esi, On triple sequence space of Bernstein operator of rough I-convergence pre-Cauchy sequences, Proyecciones, 36(4) (2017), 567-587. https://doi.org/10.4067/S0716-09172017000400567
  9. A. J. Dutta A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal., 4(2) (2013), 16-22.
  10. S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Optim., 6(1) (2015), 71-79.
  11. E. Dundar and C. Cakan, Rough I-convergence, Demonstr. Math., 47(3) (2014), 638-651. https://doi.org/10.2478/dema-2014-0051
  12. A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math., 8(2) (2007), 49-55.
  13. A. Sahiner and B. C. Tripathy, Some I-related properties of triple sequences, Selcuk J. Appl. Math., 9(2) (2008), 9-18.
  14. N. Subramanian and A. Esi, The generalized tripled difference of ${\chi}^3$ sequence spaces, Global Journal of Mathematical Analysis, 3(2) (2015), 54-60. https://doi.org/10.14419/gjma.v3i2.4412
  15. N. Subramanian and A. Esi, Rough variables of convergence, Sci. Stud. Res. Ser. Math. Inform., 27(2) (2017), 65-72.
  16. N. Subramanian and A. Esi, Wijsman rough convergence triple sequences, Mat. Stud., 48(2) (2017), 171-179.
  17. A. Esi and N. Subramanian, Generalized rough Cesaro and lacunary statistical triple difference sequence spaces in probability of fractional order defined by Musielak Orlicz function, Int. J. Anal. Appl., 16(1) (2018), 16-24.
  18. N. Subramanian and A. Esi, On triple sequence space of Bernstein operator of ${\chi}^3$ of rough ${\lambda}$-statistical convergence in probability definited by Musielak-Orlicz function p-metric, Electronic Journal of Mathematical Analysis and Applications, 6(1) (2018), 198-203.
  19. S. Velmurugan and N. Subramanian, Bernstein operator of rough ${\lambda}$-statistically and ${\rho}$ Cauchy sequences convergence on triple sequence spaces, Journal of Indian Mathematical Society, 85(1-2) (2018), 257-265.
  20. B. Hazarika, N. Subramanian and A. Esi, On rough weighted ideal convergence of triple sequence of Bernstein polynomials, Proc. Jangjeon Math. Soc., 21(3) (2018), 497-506. https://doi.org/10.17777/pjms2018.21.3.497
  21. N. Subramanian, A. Esi and M. K. Ozdemir, Rough Statistical Convergence on triple sequence of Bernstein operator of random variables in probability, Songklanakarin Journal of Science and Technology, 41(3) (2019), 567-579.
  22. N. Subramanian, A. Esi and V .A. Khan, The rough Intuitionistic fuzzy Zweier lacunary ideal convergence of triple sequence spaces, Journal of Mathematics and Statistics, 14 (2018), 72-78. https://doi.org/10.3844/jmssp.2018.72.78
  23. A. Esi and N. Subramanian, On triple sequence spaces of Bernstein operator of ${\chi}^3$ of rough ${\lambda}$-statistical convergence in probability of random variables defined by Musielak-Orlicz function, Int. J. Open Problems Compt. Math., 11(2) (2018), 62-70. https://doi.org/10.12816/0049063