**Abstract**

In this paper, we extend the notion presented by Braha (2020) in a higher dimension, we introduce the notion of *N<sup>n</sup>*,*m*,*<sup>g</sup> <sup>p</sup>*,*<sup>q</sup> C*ð Þ 1,1,1 *<sup>n</sup>*,*m*,*<sup>g</sup>* -statistically convergence and show necessity and sufficiency conditions under which the existence of the limit *st*- lim *<sup>n</sup>*, *<sup>m</sup>*, *<sup>g</sup>*!<sup>∞</sup>*xn*,*m*,*<sup>g</sup>* <sup>¼</sup> *<sup>L</sup>* follows from that *st*- lim *<sup>n</sup>*, *<sup>m</sup>*, *<sup>g</sup>*!∞*N<sup>n</sup>*,*m*,*<sup>g</sup> <sup>p</sup>*,*<sup>q</sup> C*ð Þ 1,1,1 *<sup>n</sup>*,*m*,*<sup>g</sup>* ¼ *L*. These conditions are one-sided or two-sided if *xn*,*m*,*<sup>g</sup>* is a sequence of real or complex numbers, respectively.

**Keywords:** Nörlund-Cesro summability method, one-sided and two-sided Tauberian conditions, triple statistical convergence
