Asymptotically double lacunry equivalent sequences defined by Orlicz functions

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.