1. Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
  2. Archive
  3. Volume 21, Issue 6
Year 2017, Volume 21 , Issue 6, Pages 1408 - 1412 2017-12-01

Lacunary statistical delta 2 quasi Cauchy sequences
İstatistiksel boşluklu delta 2 quasi Cauchy dizileri

Şebnem YILDIZ [1]

Abstract

The notion of a lacunary statistical d2-quasi-Cauchyness of sequence of real numbers is introduce and investigated. In this work, we present interesting theorems related to lacunary statistically d2-ward continuity. A function f, whose domain is included in R, and whose range included in R is called lacunary statistical d2 ward continuous if it preserves lacunary statistical d2 quasi-Cauchy sequences, i.e. (f(xk)) is a lacunary statistically d2 quasi-Cauchy sequence whenever (xk) is a lacunary statistically d2 quasi-Cauchy sequence, where  a sequence (xk) is called lacunary statistically d2 quasi-Cauchy if (D2 xk) is a lacunary statistically quasi-Cauchy sequence. We find out that the set of lacunary statistical d2 ward continuous functions is closed as a subset of the set of continuous functions.

Bu makalede istatistiksel boşluklu d2-quasi-Cauchy dizisi kavramı tanımlanmış ve araştırılmıştır. Bu araştırmada istatistiksel boşluklu d2-süreklilik ile ilgili ilgi çekici teoremler ispatlanmıştır. (D2xk) istatistiksel boşluklu quasi Cauchy dizisi olduğunda (xk) dizisine istatistiksel boşluklu d2-quasi-Cauchy dizisi dendiğine göre, reel sayılar kümesinin bir alt kümesi üzerinde tanımlı reel değerli bir f fonksiyonuna eğer terimleri A da olan istsatistiksel boşluklu d2-quasi-Cauchy dizilerini koruyor ise, yani (xk) dizisi terimleri A da olan istatistiksel boşluklu d2-quasi-Cauchy dizisi olduğunda (f(xk)) dizisi de istatistiksel boşluklu d2-quasi-Cauchy dizisi oluyor ise istatistiksel boşluklu d2-ward süreklidir denir. İstatistiksel boşluklu d2-ward sürekli fonksiyonların kümesinin sürekli fonksiyonlar uzayının kapalı bir alt kümesi olduğu ortaya çıkarılmıştır.

References

  • [1] H. Cakalli, “Lacunary statistical convergence in topological groups”, Indian J. Pure Appl. Math., vol. 26 no. 2, pp. 113-119, 1995. [2] H. Cakalli, “Sequential defiitions of compactness”, Appl. Math. Lett. vol. 21 no. 6, pp. 594-598, 2008. [3] H. Cakalli, “Sequential definitions of connectedness”, Appl. Math. Lett., vol. 25 no. 3, pp. 461-465, 2012.
  • [4] H. Cakalli, C.G. Aras, and A. Sonmez, “Lacunary statistical ward continuity”, AIP Conf. Proc., vol. 1676, 020042, 2015. http://dx.doi.org/10.1063/1.4930468
  • [5] H. Cakalli, and H. Kaplan, “A variation on lacunary statistical quasi Cauchy sequences”, Commun.Fac.Sci.Univ.Ank.Series A1, vol. 66, no. 2, pp. 71-79, 2017.
  • [6] J.A. Fridy, and C. Orhan, “Lacunary statistical convergence”, Pacific J. Math., vol. 160 no. 1, pp. 43-51, 1993.
  • [7] J.A. Fridy, and C. Orhan, “Lacunary statistical summability”, J. Math. Anal. Appl, vol. 173 no. 2, pp. 497-504, 1993.

Details

Subjects Mathematics
Published Date Aralık 2017
Journal Section Research Articles
Authors

Orcid: 0000-0003-3763-0308
Author: Şebnem YILDIZ
Country: Turkey
Dates

Application Date : August 25, 2017
Acceptance Date : September 11, 2017
Publication Date : December 1, 2017

Cite

Bibtex @research article { saufenbilder336128, journal = {Sakarya University Journal of Science}, issn = {}, eissn = {2147-835X}, address = {}, publisher = {Sakarya University}, year = {2017}, volume = {21}, pages = {1408 - 1412}, doi = {10.16984/saufenbilder.336128}, title = {Lacunary statistical delta 2 quasi Cauchy sequences}, key = {cite}, author = {Yıldız, Şebnem} }
APA Yıldız, Ş . (2017). Lacunary statistical delta 2 quasi Cauchy sequences . Sakarya University Journal of Science , 21 (6) , 1408-1412 . DOI: 10.16984/saufenbilder.336128
MLA Yıldız, Ş . "Lacunary statistical delta 2 quasi Cauchy sequences" . Sakarya University Journal of Science 21 (2017 ): 1408-1412 <http://www.saujs.sakarya.edu.tr/en/pub/issue/26999/336128>
Chicago Yıldız, Ş . "Lacunary statistical delta 2 quasi Cauchy sequences". Sakarya University Journal of Science 21 (2017 ): 1408-1412
RIS TY - JOUR T1 - Lacunary statistical delta 2 quasi Cauchy sequences AU - Şebnem Yıldız Y1 - 2017 PY - 2017 N1 - doi: 10.16984/saufenbilder.336128 DO - 10.16984/saufenbilder.336128 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1408 EP - 1412 VL - 21 IS - 6 SN - -2147-835X M3 - doi: 10.16984/saufenbilder.336128 UR - https://doi.org/10.16984/saufenbilder.336128 Y2 - 2017 ER -
EndNote %0 Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi Lacunary statistical delta 2 quasi Cauchy sequences %A Şebnem Yıldız %T Lacunary statistical delta 2 quasi Cauchy sequences %D 2017 %J Sakarya University Journal of Science %P -2147-835X %V 21 %N 6 %R doi: 10.16984/saufenbilder.336128 %U 10.16984/saufenbilder.336128
ISNAD Yıldız, Şebnem . "Lacunary statistical delta 2 quasi Cauchy sequences". Sakarya University Journal of Science 21 / 6 (December 2017): 1408-1412 . https://doi.org/10.16984/saufenbilder.336128
AMA Yıldız Ş . Lacunary statistical delta 2 quasi Cauchy sequences. SAUJS. 2017; 21(6): 1408-1412.
Vancouver Yıldız Ş . Lacunary statistical delta 2 quasi Cauchy sequences. Sakarya University Journal of Science. 2017; 21(6): 1408-1412.
IEEE Ş. Yıldız , "Lacunary statistical delta 2 quasi Cauchy sequences", Sakarya University Journal of Science, vol. 21, no. 6, pp. 1408-1412, Dec. 2017, doi:10.16984/saufenbilder.336128

Cited By

Authors of the Article
Şebnem YILDIZ [1]
Submit Article
Accepted Submissions
Archive
Editorial Board
Contact
TR Dizin
TR Dizin

Sakarya University Journal of Science (SAUJS)