Asymptotically ideal invariant equivalence

Abstract

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