On Asymptotically Lacunary Statistical Equivalent Sequences

Abstract

This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent, statistically limit and lacunary sequences. Let theta be a lacunary sequence; the two nonnegative sequences [x] and [y] are said to be asymptotically lacunary statistical equivalent of multiple L provided that for every is an element of> 0 lim(r) 1/h(r) broken vertical bar{k is an element of I-r: broken vertical bar X-k/yk - L broken vertical bar >= is an element of} - 0 (denoted by x similar to(sL)(0) y) and simply asymptotically lacunary statistical equivalent if L = 1. In addition, we shall also present asymptotically equivalent analogs of Fridy's and Orhan's theorems in [3].