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 ...

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 ...

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 ...

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 ...

A real valued function f defined on a subset of R, the set of real numbers is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (alpha(k)) of point in R is ...

In this paper, we introduce a concept of statistically p-quasi-Cauchyness of a real sequence in the sense that a sequence (? k ) is statistically p-quasi-Cauchy if limn›? n 1 |{k ? n: |?k+ p - ? k | ? ?}| = 0 for each ? ...

An ideal I is a family of subsets of N, the set of positive integers which is closed under taking finite unions and subsets of its elements. A sequence (x(k)) of real numbers is said to be S(I)-statistically convergent to ...

We introduce a new function space, namely the space of N-theta(p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. N-theta(alpha)(p)-ward ...

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 ...

A real function f is continuous if and only if (f(xn)) is a convergent sequence whenever (xn) is convergent and a subset E of R is compact if any sequence x = (xn) of points in E has a convergent subsequence whose limit ...