On lambda^2-asymptotically double statistical equivalent sequences

Authors

1 Adiyaman University, Science and Art Faculty, Department of Mathematics, 02040, Adiyaman, Turkey.

2 Gaziantep University, Science and Art Faculty, Department of Mathematics, 27200, Gaziantep,Turkey.

Abstract

This paper presents the following new de nition which is a natural combination of the de nition for
asymptotically double equivalent, double statistically limit and double 2􀀀 sequences. The double
sequence 2 = (m;n) of positive real numbers tending to in nity such that
m+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;
and
Im;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 be
2􀀀asymptotically double statistical equivalent of multiple L provided that for every " > 0
P 􀀀 lim
m;n
1
m;n


(k; l) 2 Im;n :

xk;l
yk;l
􀀀 L

 "

= 0
(denoted by x
SL
2 v y) and simply 2􀀀asymptotically double statistical equivalent if L = 1.