• ### Asymptotically Lacunary Statistical Equivalent Sequence Spaces Defined by Ideal Convergence and an Orlicz Function

Mahmut Karakuş1 and Tunay Bilgin2

1. Yüzüncü Yıl University, Science Faculty, Department of Mathematics. matfonks@gmail.com.

2. Yüzüncü Yıl University, Education Faculty, Department of Mathematics. tbilgin@yyu.edu.tr.

Abstract: In this study, we introduce the concepts asymptotically IpM-lacunary equivalence with order α, and asymptotically IM-lacunary statistical equivalence with order α by using a non-trivial ideal I, an Orlicz function M, and a sequence of positive real numbers p = (pk). In addition to these definitions, natural inclusion theorems where presented.

Keywords: Asymptotically equivalence, Ideal convergence, Lacunary sequence, Orlicz function