The idea ofI-convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of(Δm,I)-statistical convergence of orderαand strong(Δpm,I)-Cesàro summability of orderαof real sequences and investigated their relationship.

The main object of this article is to introduce the concepts of f-lacunary statistical convergence of order alpha and strong f-lacunary summability of order alpha of sequences of real numbers and give some inclusion relations between these spaces.