Strongly Cesaro type quasi-Cauchy sequences

Abstract

In this paper we call a real-valued function $N_{\theta }$-ward continuous if it preserves $N_{\theta }$-quasi-Cauchy sequences where a sequence $\mathbf{\alpha }=({\alpha }_k)$ is defined to be $N_{\theta }$-quasi-Cauchy when the sequence $\Delta \mathbf{\alpha }$ is in $N_{\theta }^0$. We prove not only inclusion and compactness type theorems, but also continuity type theorems.

20 pages