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In this paper, we introduce some new $I_\lambda$-lacunary statisticallyconvergent sequence spaces of order $\alpha$ defined by a Musielak-Orliczfunction. We study some relations between $I_\lambda$-lacunary statisticallyconvergence with lacunary $I_\lambda$-summable sequences. Moreover we alsostudy about the $I_\lambda$-lacunary statistically convergence of sequences intopological groups and give some important inclusion theorems.

Some new $I_\lambda$-lacunary statistical convergence