title: Some new lacunary statistical convergence with ideals.
abstract: In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space and discuss some topological properties.
authors.affiliation: Department of Mathematics, University Putra Malaysia, Serdang, 43400 Selangor, Malaysia.
authors.forename: Adem
authors.initials: A
authors.lastname: Kilicman
authors.affiliation: Department of Mathematics, University Putra Malaysia, Serdang, 43400 Selangor, Malaysia ; Department of Mathematics, Indian Institute of Technology, Bombay, Powai, 400076 Mumbai, India.
authors.forename: Stuti
authors.initials: S
authors.lastname: Borgohain
keywords: Musielak-Orlicz function; ideal convergence; lacunary sequences; probabilistic normed space