Seluk J. Appl. Math. Seluk Journal of Vol. 9. No. 2. pp. 918, 2008 Applied Mathematics Some I -related Properties of Triple Sequences Ahmet Sahiner 1 , Binod Chandra Tripathy 2 1 Department of Mathematics, Suleyman Demirel University, Cunur Campus, 32260, Isparta, Turkey e-mail: sahiner@fef.sdu.edu.tr Mathematical Sciences Division, Institute of Advanced Study in Science and Technol- ogy, Paschim Boragaon,Garchuk; Guwahati-781 035, India e-mail: tripathybc@yahoo.com Received: March 25, 2008 Abstract. Ideal convergence was presented by Kostyrko et al. in 2001. This concept was extended to the double sequences by Tripathy et al. in 2006. In this paper we introduce the notions of I -convergence, I -bounded, I -inferior and I -superior for triple sequences. We also investigate some further properties of I -limit superior and I -limit inferior of triple sequences. Key words: Double sequence; triple sequence; statistical convergence; I-convergence; double natural density; triple natural density. 2000 Mathematics Subject Classication. 40A05, 26A03 1. Preliminaries In this article we aimed to extend the notion of statistically convergent triple sequences to Iconvergent triple sequences. Now we recall some denitions and notions introduced in [14]. Denition 1. A function x : N  N  N ! R (C) is called a real(complex) triple sequence. Denition 2. A triple sequence (x nkl ) is said to be convergent to L in Pring- sheims sense if for every "> 0; there exists n 0 (") 2 N such that jx nkl  Lj <" whenever n; k; l  n 0 . Denition 3. A triple sequence (x nkl ) is said to be Cauchy sequence if for every "> 0; there exists n 0 (") 2 N such that jx pqr  x nkl j <" whenever p  n  n 0 ; q  k  n 0 ;r  l  n 0 .