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Now showing items 1-10 of 31

#### Ward Continuity in 2-Normed Spaces

(UNIV NIS, FAC SCI MATH, 2015)

In this paper, we introduce and investigate the concept of ward continuity in 2-normed spaces. A function f defined on a 2-normed space (X, parallel to., .parallel to) is ward continuous if it preserves quasi-Cauchy ...

#### 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 ...

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

(American Institute of Physics Inc., 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 ...

#### Lacunary statistically upward half quasi-Cauchy sequences

(AMER INST PHYSICS, 2015)

A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi -Cauchy sequences where a sequence (x,) of ...

#### Sequential definitions of connectedness

(PERGAMON-ELSEVIER SCIENCE LTD, 2012)

We investigate the impact of changing the definition of convergence of sequences on the structure of the set of connected subsets of a topological group, X. A non-empty subset A of X is called G-sequentially connected if ...

#### A variation on strong lacunary quasi-Cauchy sequences in 2-normed spaces

(American Institute of Physics Inc., 2015)

In this paper, we introduce and investigate ideal strong lacunary ward continuity in 2-normed spaces. A function f on a subset A of a 2-normed space X into X is ideal strongly lacunary ward continuous if it preserves ideal ...

#### Lacunary statistical ward continuity

(AMER INST PHYSICS, 2015)

The main object of this paper is to investigate lacunary statistically ward continuity. We obtain some relations between this kind of continuity and some other kinds of continuities. It turns out that any lacunary statistically ...

#### Beyond Cauchy and Quasi-Cauchy Sequences

(UNIV NIS, FAC SCI MATH, 2018)

In this paper, we investigate the concepts of downward continuity and upward continuity. A real valued function on a subset E of R, the set of real numbers, is downward continuous if it preserves downward quasi-Cauchy ...

#### N-alpha(beta)(theta, I)- Ward Continuity

(AMER INST PHYSICS, 2019)

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (alpha, beta) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (alpha, beta) is ...

#### 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. ...