On I− Lacunary Statistical Convergence of Order α of Sequences of Sets

Abstract

The idea ofI−convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P. ; Sal´at, ˇ T. and Wilczy ´nski, 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 α and Wijsman strongly I−lacunary statistical convergence of order α, and investigated between their relationship