Asymptotically double lacunry equivalent sequences defined by Orlicz functions - Esi, Ayhan (Acta Scientiarum. Technology, 2014)
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 Îµ>0, P-lim_k,lM(((|((x_k,l)/(y_k,l))-L|)/Ï))=0, for some Ï>0, (denoted by xâˆ½y) and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems. Â Â Â