Some new lacunary statistical convergence with ideals

Adem Kilicman; Stuti Borgohain

doi:10.1186/s13660-016-1284-9

Some new lacunary statistical convergence with ideals

J Inequal Appl. 2017;2017(1):15. doi: 10.1186/s13660-016-1284-9. Epub 2017 Jan 10.

Authors

Adem Kilicman¹, Stuti Borgohain²

Affiliations

¹ Department of Mathematics, University Putra Malaysia, Serdang, 43400 Selangor, Malaysia.
² Department of Mathematics, University Putra Malaysia, Serdang, 43400 Selangor, Malaysia ; Department of Mathematics, Indian Institute of Technology, Bombay, Powai, 400076 Mumbai, India.

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.

Keywords: Musielak-Orlicz function; ideal convergence; lacunary sequences; probabilistic normed space.