On IΔ-deferred statistically rough convergence with order α

Abstract

In this article, we introduce the concept of IΔ-deferred statistically rough convergence of order α, (0 < α ≤ 1) in a normed linear space. We mainly examine various properties such as closedness and convexity of the set of I − DSr,αp,q (Δ)−limit for a sequence. Besides this, we prove a necessary and sufficient condition for the I −DSr,αp,q (Δ)−convergence of a real valued sequence and derive some interesting implication relationships.