A new study on the strongly lacunary quasi Cauchy sequences

In this paper, the concept of a strongly lacunary δ2 quasi-Cauchy sequence is introduced. We proved interesting theorems related to strongly lacunary δ2-quasi-Cauchy sequences. A real valued function f defined on a subset A of the set of real numbers, is strongly lacunary δ2 ward continuous on A if it preserves strongly lacunary δ2 quasi-Cauchy sequences of points in A, i.e. (f(αk)) is a strongly lacunary δ2 quasi-Cauchy sequence whenever (αk) is a strongly lacunary δ2 quasi-Cauchy sequences of points in A, where a sequence (αk) is called strongly lacunary δ2 quasi-Cauchy if (Δ2αk) is a strongly lacunary δ2 quasi-Cauchy sequence where Δ2αk = αk+2 − 2αk+1 + αk for each positive integer k.