Abstract:
This paper presents the following definition which is natural combination of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences x = (x(k,l)) and y(y(k,l)) are said to be M-asymptotically double equivalent to multiple L provided that for every epsilon > 0 P-lim(k,l)M(vertical bar x(k,l)/y(k,l)vertical bar-L/rho) = 0 for some rho > 0 (denoted by (M) x similar to y and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems.
