Asymptotically ideal invariant equivalence

In this paper, the concepts of asymptotically -equivalence, -asymptotically equivalence, st\-rong\-ly -asymptotically equivalence and strongly -asymptotically -equivalence for real number sequences are de\-fi\-ned. Also, we give relationships among these new type equivalence concepts and the concept of \linebreak -asymptotically equivalence which is studied in [Savaş, E. and Patterson, R. F., -asymptotically lacunary statistical equivalent sequences, Cent. Eur. J. Math., 4 (2006), No. 4, 648–655].