On lambda^2-asymptotically double statistical equivalent sequences

Abstract

This paper presents the following new de nition which is a natural combination of the de nition forasymptotically double equivalent, double statistically limit and double 2􀀀 sequences. The doublesequence 2 = (m;n) of positive real numbers tending to in nity such thatm+1;n  m;n + 1; m;n+1  m;n + 1;m;n 􀀀 m+1;n  m;n+1 􀀀 m+1;n+1; 1;1 = 1;andIm;n = f(k; l) : m 􀀀 m;n + 1  k  m; n 􀀀 m;n + 1  l  ng :For double 2􀀀sequence; the two non-negative sequences x = (xk;l) and y = (yk;l) are said to be2􀀀asymptotically double statistical equivalent of multiple L provided that for every > 0P 􀀀 limm;n1m;n (k; l) 2 Im;n : xk;lyk;l􀀀 L   = 0(denoted by xSL2 v y) and simply 2􀀀asymptotically double statistical equivalent if L = 1.