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#### Variations on rho statistical quasi cauchy sequences

(AMER INST PHYSICS, 2019)

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 ...

#### Upward and Downward Statistical Continuities

(UNIV NIS, FAC SCI MATH, 2015)

A real valued function f defined on a subset E of R, the set of real numbers, is statistically upward (resp. downward) continuous if it preserves statistically upward (resp. downward) half quasi-Cauchy sequences; A subset ...

#### A variation on ward continuity

(UNIV NIS, FAC SCI MATH, 2013)

In this paper, we prove that any ideal ward continuous function is uniformly continuous either on an interval or on an ideal ward compact subset of R. A characterization of uniform continuity is also given via ideal ...

#### On variations on quasi Cauchy sequences in metric spaces

(AMER INST PHYSICS, 2019)

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 ...

#### Variations on Quasi-Cauchy Sequences

(UNIV NIS, FAC SCI MATH, 2015)

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 ...

#### Abel statistical delta quasi Cauchy sequences

(AMER INST PHYSICS, 2019)

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, ...

#### Ideal quasi-Cauchy sequences

(SPRINGER INTERNATIONAL PUBLISHING AG, 2012)

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. A sequence (x(n)) of real numbers is said to be I-convergent to a real number L if for each ...

#### 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 ...