Beyond the quasi-Cauchy sequences beyond the Cauchy sequences
In this paper, we investigate the concept of upward continuity. A real valued function on a subset E of R, the set of real numbers is upward continuous if it preserves upward quasi Cauchy sequences in E, where a sequence (xk) of points in R is called upward quasi Cauchy if for every ? > 0 there exists a positive integer n0 such that xn - xn+1 < ? for n ? n0. It turns out that the set of upward continuous functions is a proper subset of the set of continuous functions. © 2016 Author(s).