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In this paper, we introduce and investigate ideal strong lacunary ward continuity in 2-normed spaces. A function f on a subset A of a 2-normed space X into X is ideal strongly lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences of points in A. We also studied some other kinds of continuities. [ABSTRACT FROM AUTHOR]

In this extended abstract, we introduce the concept of delta quasi Cauchy sequences in metric spaces. A function f defined on a subset of a metric space X to X is called delta ward continuous if it preserves delta quasi Cauchy sequences, where a sequence (xk) of points in X is called delta quasi Cauchy if lim n → ∞ [ d (x k + 2 , x k + 1) − d (x k + 1 , x k) ] = 0. A new type compactness in terms of δ-quasi Cauchy sequences, namely δ-ward compactness is also introduced, and some theorems related to δ-ward continuity and δ-ward compactness are obtained. Some other types of continuities are also discussed, and interesting results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the concept of Abel statistical delta ward compactness and Abel statistical delta ward continuity in metric spaces. A function f defined on a metric space X into X is called Abel statistically delta ward continuous it preserves Abel statistical delta quasi Cauchy sequences, where a sequence (xk) of points in X is called Abel statistically delta quasi Cauchy if lim x → 1 − (1 − x) ∑ k : | d (x k + 2 , x k + 1 − d (x k + 1 , x k ) | ≥ ε x k = 0 for every ε > 0, Some other types of compactnesses are also studied and interesting results are obtained. [ABSTRACT FROM AUTHOR]

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 : | | Δ x k , z | | ≥ ε x k = 0 for every ε > 0 and z ∈ X, where Δxk = xk+1 − xk for every k ∈ N. Some other types of compactness and continuities are also studied and interesting results are obtained. [ABSTRACT FROM AUTHOR]