A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (x(n)) statistically quasi-Cauchy if st - lim(n ->infinity) d(x(n+1), x(n)) = ...

Recently, it has been proved that a real-valued function defined on a subset E of A. the set of real numbers, is uniformly continuous on E if and only if it is defined on E and preserves quasi-Cauchy sequences of points ...

Recently, it has been proved that a real-valued function defined on an interval A of R, the set of real numbers, is uniformly continuous on A if and only if it is defined on A and preserves quasi-Cauchy sequences of points ...

A function f on a topological space is sequentially continuous at a point u if, given a sequence (x(n)), lim x(n) = u implies that lim f (x(n)) f (u). This definition was modified by Connor and Grosse-Erdmann for real ...

In this paper, we investigate slowly oscillating continuity in cone metric spaces. It turns out that the set of slowly oscillating continuous functions is equal to the set of uniformly continuous functions on a slowly ...

Recently, the concept of N-theta-ward continuity was introduced and studied. In this paper, we prove that the uniform limit of N-theta-ward continuous functions is N-theta-ward continuous, and the set of all N-theta-ward ...

A sequence (x(n)) of points in a topological group is called Delta-quasi-slowly oscillating if (Delta x(n)) is quasi-slowly oscillating, and is called quasi-slowly oscillating if (Delta x(n)) is slowly oscillating. A ...

A sequence (x(n)) of points in a topological group is slowly oscillating if for any given neighborhood U of 0, there exist delta = delta(U) > 0 and N = N(U) such that x(m)-x(n) epsilon U if n >= N(U) and n <= m <= (1+delta)n. ...

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 ...

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied ...