초록

In this paper, using the concept of natural density, we introduce the notion of arithmetic rough statistical convergence of triple sequences. We define the set of arithmetic rough statistical limit points of a triple sequence and obtain arithmetic rough statistical convergence criteria associated with this set. Later, we prove this set is closed and convex and also examine the relations between the set of arithmetic rough statistical cluster points and the set of arithmetic rough statistical limit points of a triple sequence.

키워드

Arithmetic rough statistical convergence, Summability, natural density, Triple sequences, Chi sequence

참고문헌(18)open

  1. [학술지] S. Aytar / 2008 / Rough statistical Convergence / Numer. Funct. Anal. Optimi 29 (3) : 291 ~ 303

  2. [학술지] A. J. Dutta / 2013 / Statistically convergent triple sequence spaces defined by Orlicz function / J. Math. Anal 4 (2) : 16 ~ 22

  3. [학술지] S. Debnath / 2015 / Some generalized triple sequence spaces of real numbers / J. Nonlinear Anal. Optimi 6 (1) : 71 ~ 79

  4. [학술지] A. Esi / 2014 / On some triple almost lacunary sequence spaces defined by Orlicz functions / Research and Reviews : Discrete Mathematical Structures 1 (2) : 16 ~ 25

  5. [학술지] A. Esi / 2014 / Almost convergence of triple sequences / Global J. Math. Anal 2 (1) : 6 ~ 10

  6. [학술지] A. Esi / 2015 / On lacunary statistically convergent triple sequences in probabilistic normed space / Appl. Math. Inf. Sci 9 (5) : 2529 ~ 2534

  7. [학술지] A. Esi / 2018 / On triple sequence space of Bernstein-Stancu operator of rough $I_{\lambda}% -$statistical convergence of weighted $g\left( A\right) $ / ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 16 (3) : 337 ~ 361

  8. [학술지] H. Fast / 1951 / Sur la convergence statistique / Colloq. Math 2 : 241 ~ 244

  9. [학술지] S. K. Pal / 2013 / Rough ideal Convergence / Hacee. J. Math. and Stat 42 (6) : 633 ~ 640

  10. [학술지] H. X. Phu / 2001 / Rough convergence in normed linear spaces / Numer. Funct. Anal. Optimi 22 : 201 ~ 224

  11. [학술지] A. Sahiner / 2007 / Triple sequences and their statistical convergence / Selcuk J. Appl. Math 8 (2) : 49 ~ 55

  12. [학술지] A. Sahiner / 2008 / Some I related properties of triple sequences / Selcuk J. Appl. Math 9 (2) : 9 ~ 18

  13. [학술지] H. Steinhaus / 1951 / Sur la convergence ordinaire et la convergence asymptotique / Colloq. Math 2 : 73 ~ 74

  14. [학술지] N. Subramanian / 2015 / The generalized tripled di erence of 3 sequence spaces / Global Journal of Mathematical Analysis 3 (2) : 54 ~ 60

  15. [학술지] B. C. Tripathy / 2015 / Vector valued multiple sequences defined by Orlicz functions / Boletim da Sociedade Paranaense de Matematica 33 (1) : 67 ~ 79

  16. [학술지] B. C. Tripathy / 2015 / Multiple sequences in probabilistic normed spaces / Afrika Matematika 26 (5-6) : 753 ~ 760

  17. [학술지] B. C. Tripathy / 2015 / Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed space / Afrika Matematika 26 (7-8) : 1281 ~ 1289

  18. [학술지] B. C. Tripathy / 2016 / Statistically convergent multiple sequences in probabilistic normed spaces / U.P.B. Sci. Bull., Ser.A 78 (4) : 83 ~ 94