On asymptotically equivalent difference sequences with respect to a modulus function

摘要

This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence and Δ m -lacunary strongly summable with respect to a modulus f. Using this definitions we have proved the (f, Δ m )-asymptotically equivalence and Δ m -lacunary statistical asymptotically equivalence analogues of theorems of Tripathy and Et (Stud Univ Babeş-Bolyai Math (1):119–130, 2005) and Çolak’s theorems (Filomat 17:9–14, 2003).