A New Variation on Lacunary Statistical Quasi Cauchy Sequences

Abstract

In this paper, the concept of an S-theta-delta(2)-quasi-Cauchy sequence is investigated. In this investigation, we proved interesting theorems related to S-theta-delta(2)-ward continuity, and some other kinds of continuities. A real valued function f defined on a subset A of R, the set of real numbers, is called S-theta-delta(2)-ward continuous on A if it preserves S-theta-delta(2)-quasi-Cauchy sequences of points in A, i.e. (f (alpha(k))) is an S-theta-delta(2)-quasi-Cauchy sequence whenever (alpha(k)) is an S-theta-delta(2)-quasi-Cauchy sequence of points in A, where a sequence (alpha(k)) is called S-theta-delta(2)-quasi-Cauchy if (Delta(2)alpha(k)) is an S-theta- quasi-Cauchy sequence. It turns out that the set of S-theta-delta(2)-ward continuous functions is a closed subset of the set of continuous functions.