ON WIJSMAN I− LACUNARY STATISTICAL EQUIVALENCE OF ORDER (η, µ)

Abstract

The idea of asymptotically equivalent sequences and asymptotic regular matrices was introduced by Marouf [ Marouf, M. Asymptotic equivalence and summability, Int. J. Math. Sci. 16(4) 755-762 (1993) ] and Patterson [ Patterson, RF. On asymptotically statistically equivalent sequences, Demonstr. Math. 36(1), 149-153 (2003) ] extended these concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for nonnegative summability matrices. In this paper we introduce the concepts of Wijsman asymptotically I−lacunary statistical equivalence of order (η, µ) and strongly asymptotically I−lacunary equivalence of order (η, µ) of sequences of sets and investigated between their relationship.