Some new $I_{\lambda }$-lacunary statistical convergence

Abstract

In this paper, we introduce some new $I_{\lambda }$-lacunary statistically convergent sequence spaces of order $\alpha$ defined by a Musielak-Orlicz function. We study some relations between $I_{\lambda }$-lacunary statistically convergence with lacunary $I_{\lambda }$-summable sequences. Moreover we also study about the $I_{\lambda }$-lacunary statistically convergence of sequences in topological groups and give some important inclusion theorems.

11 pages