### 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 *µ * 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 $ \epsilon > 0 $

$\lim_r(1/h_r)|{k\in I_r : |(x_k /y_k)-L|\geq \epsilon }|=0 $

(denoted by $x \sim^{S^L_\theta} y$ 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].

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