DOI QR코드

DOI QR Code

ROUGH STATISTICAL CONVERGENCE OF DIFFERENCE DOUBLE SEQUENCES IN NORMED LINEAR SPACES

  • KISI, Omer (Bartin University Faculty of Science Depertmant of Mathematics) ;
  • UNAL, Hatice Kubra (Bartin University Graduate School of Natural and Applied Science)
  • 투고 : 2020.08.31
  • 심사 : 2021.02.15
  • 발행 : 2021.03.25

초록

In this paper, we introduce rough statistical convergence of difference double sequences in normed linear spaces as an extension of rough convergence. We define the set of rough statistical limit points of a difference double sequence and analyze the results with proofs.

키워드

참고문헌

  1. H. Fast, Sur la convergenc statistique, Colloq. Math. 2 (1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  2. M. Mursaleen, O.H.H. Edely, Statistical convergence of double sequence, J. Math. Anal. Appl. 288 (2003), 223-231. https://doi.org/10.1016/j.jmaa.2003.08.004
  3. S. Yegul and E. Dundar, Statistical convergence of double sequences of functions and some properties in 2-normed spaces, Facta Univ. Ser. Math. Inform. 33 (5) (2018), 705-719.
  4. M. Gurdal and S. Pehlivan, The statistical convergence in 2-Banach spaces, Thai J. Math. 2 (1) (2004), 107-113.
  5. M. Gurdal and S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bull. Math. 33 (2009), 257-264.
  6. P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Anal. Exchange, 26 (2) (2000), 669-686. https://doi.org/10.2307/44154069
  7. P. Kostyrko, M. Macaj, T. Salat and M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443-464.
  8. E. Savas and M. Gurdal, I-statistical convergence in probabilistic normed space, Sci. Bull. Series A Appl. Math. Physics, 77 (4) (2015), 195-204.
  9. M. Gurdal and M.B Huban, On I-convergence of double sequences in the Topology induced by random 2-norms, Mat. Vesnik, 66 (1) (2014), 73-83.
  10. M. Gurdal and A. Sahiner, Extremal I-limit points of double sequences, Appl. Math. E-Notes, 8 (2008), 131-137.
  11. E. Savas and M. Gurdal, Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Syst. 27 (4) (2014), 1621-1629. https://doi.org/10.3233/IFS-141128
  12. E. Savas and M. Gurdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia, 41 (2015), 289-294. https://doi.org/10.2306/scienceasia1513-1874.2015.41.289
  13. E. Savas and P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24 (2011), 826-830. https://doi.org/10.1016/j.aml.2010.12.022
  14. M. Mohiuddine and B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat, 31 (6) (2017), 1827-1834. https://doi.org/10.2298/FIL1706827M
  15. M. Mursaleen and S.A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca 62 (1) (2012), 49-62. https://doi.org/10.2478/s12175-011-0071-9
  16. M. Mursaleen, S. Debnath and D. Rakshit, I-statistical limit superior and I-statistical limit inferior, Filomat, 31 (7) (2017), 2103-2108. https://doi.org/10.2298/FIL1707103M
  17. E. Dundar and O. Talo, I2-convergence of double sequences of fuzzy numbers, Iran. J. Fuzzy Syst. 10 (3) (2013), 37-50.
  18. M. Arslan and E. Dundar, On I-convergence of sequences of functions in 2-normed spaces, Southeast Asian Bull. Math. 42 (2018), 491-502.
  19. E. Dundar and B. Altay, Multipliers for bounded I2-convergence of double sequences, Math. Comput. Model. 55 (3-4) (2012), 1193-1198. https://doi.org/10.1016/j.mcm.2011.09.043
  20. E. Dundar and N. P. Akin, Wijsman lacunary ideal invariant convergence of double sequences of sets, Honam Math. J. 42 (2) (2020), 345-358. https://doi.org/10.5831/HMJ.2020.42.2.345
  21. E. Dundar, N. P. Akin, Wijsman lacunary ideal invariant convergence of double sequences of sets, Honam Math. J. 42 2 (2020), 345-358. https://doi.org/10.5831/HMJ.2020.42.2.345
  22. H. Gumus and F. Nuray, ∆m-Ideal convergence, Selcuk J. Appl. Math. 12 (2) (2011), 101-110.
  23. S. Debnath and J. Debnath, On I-statistically convergent sequence spaces defined by sequences of Orlicz functions using matrix transformation, Proyecciones, 33 (3) (2014), 277-285. https://doi.org/10.4067/s0716-09172014000300004
  24. M. Et, A. Alotaibi and S. A. Mohiuddine, On (∆m-I)-statistical convergence of order α, Sci. World J. (2014), Article ID 535419 5 pages.
  25. H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim. 22 (2001), 199-222. https://doi.org/10.1081/NFA-100103794
  26. H. X. Phu, Rough continuity of linear operators, Numer. Funct. Anal. Optim. 23 (2002), 139-146. https://doi.org/10.1081/NFA-120003675
  27. H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Optim. 24 (2003), 285-301. https://doi.org/10.1081/NFA-120022923
  28. M. Arslan and E. Dundar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl. 10 (3) (2018), 1-9.
  29. S. Aytar, Rough statistical convergence, Numer. Funct. Anal. Optim. 29 (3-4) (2008), 291-303. https://doi.org/10.1080/01630560802001064
  30. 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
  31. S.K. Pal, D. Chandra and S. Dutta, Rough ideal convergence, Hacet. J. Math. Stat. 42 (6) (2013), 633-640.
  32. P. Malik, M. Maity, On rough convergence of double sequences in normed linear spaces, Bull. Allahabad Math. Soc. 28 (1) (2013), 89-99.
  33. P. Malik, M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afr. Mat. 27, (2016), 141-148. https://doi.org/10.1007/s13370-015-0332-9
  34. E. Dundar and C. Cakan, Rough I-convergence, Gulf J. Math. 2 (1) (2014), 45-51.
  35. E. Dundar and C. Cakan, Rough convergence of double sequences, Demonstr. Math. 47 (3) (2014), 638-651. https://doi.org/10.2478/dema-2014-0051
  36. E. Dundar, On Rough I2-convergence, Numer. Funct. Anal. Optim. 37 (4) (2016), 480-491. https://doi.org/10.1080/01630563.2015.1136326
  37. E. Savas, S. Debnath and D. Rakshit, On I-statistically rough convergence, Publ. Inst. Math. 105 (119) (2019), 145-150. https://doi.org/10.2298/PIM1919145S
  38. M. Arslan and E. Dundar, On rough convergence in 2-normed spaces and some properties, Filomat, 33 (16) (2019), 5077-5086, https://doi.org/10.2298/fil1916077a
  39. O. Kisi and E. Dundar, Rough I2-lacunary statistical convergence of double sequences, J. Inequal. Appl. 2018:230 (2018), 16 pages.
  40. N. Demir and H. Gumus, Rough convergence for difference sequences, New Trends Math. Sci. 2 (8) (2020), 22-28 https://doi.org/10.20852/ntmsci.2020.402
  41. N. Demir and H. Gumus, Rough statistical convergence for difference sequences, Kragujevac J. Math. 46 (5) (2022), 733-742.
  42. H. Gumus and N. Demir, ∆I-Rough convergence, under review.
  43. O. Kisi and E. Dundar, Rough ∆I-statistical convergence, Numer. Funct. Anal. Optim. (to appear).
  44. O. Kisi, H. Kubra Unal, Rough ∆I2-statistical convergence of double difference sequences in normed linear spaces, Bull. Math. Anal. Appl. 12 (1) (2020), 1-11.
  45. O. Kisi, Rough ∆I2-convergence of double difference sequences, Ann. Fuzzy Math. Inform. 20 (2) (2020), 105-114. https://doi.org/10.30948/AFMI.2020.20.2.105