Strongly lacunary δ-quasi-Cauchy sequences in 2-normed spaces

A sequence (xk ) of points in a subset E of a 2-normed space X is called strongly lacunary δ-quasi-Cauchy, or Nθ-δ-quasi-Cauchy if (Δxk) is Nθ-convergent to 0, that is limr→∞1hr∑k∈Ir||Δ2xk,z||=0 for every fixed z ∈ X. A function defined on a subset E of X is called strongly lacunary δ-ward continuous if it preserves Nθ-δ-quasi-Cauchy sequences, i.e. ( f (xk )) is an Nθ-δ-quasi-Cauchy sequence whenever (xk ) is. In this study we obtain some theorems related to strongly lacunary δ-quasi-Cauchy sequences.