On I-lacunary statistical convergence of order α of sequences of sets

Abstract

The idea of I-convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P. ; Sal?t, T. and Wilczy?ski, W. I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle,W. H. Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245(2) (2000), 513-527]. In this paper we introduce the concepts of Wijsman I-lacunary statistical convergence of order ? and Wijsman strongly I-lacunary statistical convergence of order ?, and investigated between their relationship.