$\Delta^{m}$-lacunary Statistical Convergence of Order $\alpha$ Defined by a Modulus Function
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Keywords:
Statistical convergence, Lacunary sequence, Lacunary refinment, modulus functionAbstract
In this paper, we introduce the concepts of lacunary $\Delta^{m}$-statistically convergent sequence of order $\alpha$ and strongly
$N_{\theta}^{\alpha}(\Delta^{m},f,p)$-summable sequences of order $\alpha$ are introduced. Some inclusion relations between the set of lacunary $\Delta^{m}$-statistically convergent sequences of order $\alpha$ and strongly $N_{\theta}^{\alpha}(\Delta^{m},f,p)$-summable sequences of order $\alpha$ and the relations between two arbitrary lacunary sequences are discussed.
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