Abel statistical quasi Cauchy sequences in 2-normed spaces

摘要

In this paper, we investigate the concept of Abel statistical ward continuity in 2-normed spaces. A function f defined on a 2-normed space X into X is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (xk) of points in X is called Abel statistically quasi Cauchy if lim_(x→1)-(1-x)∑_(k:‖Δxk,z‖≥ε) x~k=0 for every ε > 0 and z ∈ X, where Δ_(xk) = x_(k+1) - x_k for every k ∈ N. Some other types of compactness and continuities are also studied and interesting results are obtained.