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 ...

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 ...

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 ...

Recently, the first author has introduced a concept of G-sequential connectedness in the sense that a non-empty subset A of a Hausdorff topological group X is G-sequentially connected if the only subsets of A which are ...

In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function f on a subset E of R, the set of real numbers is down continuous if it preserves downward half Cauchy ...

In this paper we introduce the concepts of Wijsman (f, I) -lacunary statistical convergence of order alpha and Wijsman strongly (f, I) -lacunary statistical convergence of order alpha, and investigated between their relationship.

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 ...

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 ...

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 ...

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are ...