Strongly Cesaro type quasi-Cauchy sequences

In this paper we call a real-valued function $N_θ$-ward continuous if it preserves $N_θ$-quasi-Cauchy sequences where a sequence $\boldsymbolα=(α_{k})$ is defined to be $N_θ$-quasi-Cauchy when the sequence $Δ\boldsymbolα$ is in $N^{0}_θ$. We prove not only inclusion and compactness type theorems, but also continuity type theorems.

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