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#### Statistical quasi-Cauchy sequences

(PERGAMON-ELSEVIER SCIENCE LTD, 2011)

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)) = ...

#### delta-quasi-Cauchy sequences

(PERGAMON-ELSEVIER SCIENCE LTD, 2011)

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 ...

#### Statistical ward continuity

(PERGAMON-ELSEVIER SCIENCE LTD, 2011)

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 ...

#### On G-continuity

(PERGAMON-ELSEVIER SCIENCE LTD, 2011)

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 ...

#### Slowly oscillating continuity in abstract metric spaces

(UNIV NIS, FAC SCI MATH, 2013)

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 ...

#### A Study on N-theta-Quasi-Cauchy Sequences

(HINDAWI LTD, 2013)

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 ...

#### On Delta-quasi-slowly oscillating sequences

(PERGAMON-ELSEVIER SCIENCE LTD, 2011)

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 ...

#### New kinds of continuities

(PERGAMON-ELSEVIER SCIENCE LTD, 2011)

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. ...

#### FORWARD CONTINUITY

(EUDOXUS PRESS, LLC, 2011)

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 ...

#### On an equivalence of topological vector space valued cone metric spaces and metric spaces

(PERGAMON-ELSEVIER SCIENCE LTD, 2012)

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 ...