Rough statistical convergence on triple sequences

  • Shyamal Debnath Tripura University.
  • N. Subramanian SASTRA University.


In this paper, using the concept of natural density, we introduce the notion of rough statistical convergence of triple sequences. We define the set of rough statistical limit points of a triple sequence and obtain 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 rough statistical cluster points and the set of rough statistical limit points of a triple sequence.

Biografía del autor

Shyamal Debnath, Tripura University.
Department of Mathematics.
N. Subramanian, SASTRA University.
Department of Mathematics.


[1] S. Aytar Rough statistical Convergence, Numer. Funct. Anal. Optimi., 29 (3), pp. 291-303, (2008).

[2] A. J. Datta A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J Math. Anal., 4 (2), pp. 16-22, (2013).

[3] S. Debnat, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Optimi., 6(1), (2015), 71-79.

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

[5] A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global J. Math. Anal., 2 (1), pp. 6-10, (2014).

[6] A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9 (5), pp. 2529-2534, (2015).

[7] H. Fast, Sur la convergence statistique, Colloq. Math. 2, pp. 241-244, (1951).

[8] S. K. Pal, D. Chandra and S. Dutta Rough ideal Convergence, Hacee. J. Math. and Stat., 42 (6), pp. 633-640, (2013).

[9] H. X. Phu Rough convergence in normed linear spaces, Numer. Funct. Anal. Optimi., 22, pp. 201-224, (2001).

[10] A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math. , 8 (2), pp. 49-55, (2007).

[11] A. Sahiner, B. C. Tripathy, Some I related properties of triple sequences, Selcuk J. Appl. Math. , 9 (2), pp. 9-18, (2008).

[12] H.Steinhaus Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, pp. 73-74, (1951).

[13] N. Subramanian and A. Esi, The generalized tripled difference of χ3 sequence spaces, Global Journal of Mathematical Analysis, 3 (2), pp. 54-60, (2015).
Cómo citar
Debnath, S., & Subramanian, N. (1). Rough statistical convergence on triple sequences. Proyecciones. Revista De Matemática, 36(4), 685-699. Recuperado a partir de

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