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Now showing items 1-10 of 61

#### 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. ...

#### A New Variation on Statistically Quasi Cauchy Sequences

(AMER INST PHYSICS, 2018)

A sequence (alpha(k)) of real numbers is called lambda-statistically upward quasi-Cauchy if for every epsilon > 0 lim(n ->infinity 1/)lambda(n)vertical bar{k is an element of I-n : alpha(k) - alpha(k+1) >= epsilon}vertical ...

#### A Variation on Statistical Ward Continuity

(MALAYSIAN MATHEMATICAL SCIENCES SOC, 2017)

A sequence (alpha(k)) of points in R, the set of real numbers, is called rho-statistically convergent to an element l of R if lim (n ->infinity) 1/rho n |{k <= n : |alpha(k)-l| >= epsilon}| = 0 for each epsilon > 0, where ...

#### A variation on arithmetic continuity

(SOC PARANAENSE MATEMATICA, 2017)

A sequence (x(k)) of points R, the set of real numbers, is called arithmetically convergent if for each epsilon > 0 there is an lat for every integer m, we have vertical bar x(m) - x(<m,n>)vertical bar < epsilon, where k ...

#### 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 ...

#### N-theta-Ward Continuity

(HINDAWI LTD, 2012)

A function f is continuous if and only if f preserves convergent sequences; that is, (f(alpha(n))) is a convergent sequence whenever (alpha(n)) is convergent. The concept of N-theta-ward continuity is defined in the sense ...

#### 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 ...

#### Beyond the quasi-Cauchy sequences beyond the Cauchy sequences

(AMER INST PHYSICS, 2016)

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 ...

#### 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 ...

#### 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 ...