On I-Lacunary Statistical Convergence of Order Alpha of Sequences of Sets

Abstract

     The idea of I-convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P. ; Šalát, T. and Wilczyński, 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 alpha  and Wijsman strongly I-lacunary statistical convergence of order alpha, and investigated between their relationship.