A sequence (alpha(k)) of points in R, the set of real numbers, is called rho-statistically p quasi Cauchy if lim(n ->infinity )1/rho(n) vertical bar{k <= n : vertical bar Delta(p)alpha(k)vertical bar >= epsilon}vertical ...

For a fixed positive integer p. a sequence (x(n)) in a metric space X is called p-quasi-Cauchy if (Delta(p)x(n)) is a null sequence where Delta(p)x(n) = d(x(n+p), x(n)) for each positive integer n. A subset E of X is called ...

In this paper, we introduce and study new kinds of continuities. It turns out that a function f defined on an interval is uniformly continuous if and only if there exists a positive integer p such that f preserves ...

In this paper, we investigate the concept of Abel statistical delta quasi Cauchy sequences. A real function! is called Abel statistically delta ward continuous it preserves Abel statistical delta quasi Cauchy sequences, ...

A real function f is continuous if and only if (f(x(n))) is a convergent sequence whenever (x(n)) is convergent and a subset E of R is compact if any sequence x = (x(n)) of points in E has a convergent subsequence whose ...