Some new $I_λ$-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.