A variation on strongly lacunary delta ward continuity in 2-normed spaces

Abstract

A sequence (x k ) of points in a subset E of a 2-normed space X is called strongly lacunary δ-quasi-Cauchy, or N θ -δ-quasi-Cauchy if (∆x k ) is N θconvergent to 0, that is limr→∞ 1 hr k∈Ir ||∆ 2 x k , 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 N θ -δ-quasi-Cauchy sequences, i.e. (f (x k )) is an N θ -δ-quasi-Cauchy sequence whenever (x k ) is. In this study we obtain some theorems related to strongly lacunary δ-quasi-Cauchy sequences.