<b>Asymptotically double lacunry equivalent sequences defined by Orlicz functions<b>

Abstract

This paper presents the following definition which is natural combition 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 ε>0, P-lim_{k,l}M(((|((x_{k,l})/(y_{k,l}))-L|)/Ï))=0, for some Ï>0, (denoted by x∽y) and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems.