Wijsman Orlicz Asymptotically Ideal ϕ-Statistical Equivalent Sequences

Abstract EN

An ideal I is a family of subsets of positive integers ℕ which is closed under taking finite unions and subsets of its elements.

In this paper, we introduce a new definition of asymptotically ideal ϕ-statistical equivalent sequence in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, ϕ-statistical equivalent sequences in Wijsman sense.

Finally, we introduce the notion of Cesaro Orlicz asymptotically ϕ-equivalent sequences in Wijsman sense and establish their relationship with other classes.