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.
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机译：在这种扩展的摘要中，我们在公制空间中介绍了Delta Quasi Cauchy序列的概念。 在度量空间X到X的子集上定义的函数f称为Delta Drow，如果保留Delta准Cauchy序列，其中x中点的序列（XK）称为Delta Quasi Cauchy，则为Lim_（n→∞）[ D（x_（k + 2），x_（k + 1））-d（x_（k + 1），x_k）] = 0。 还引入了Δ-Quasi Cauchy序列方面的新型紧凑性，即Δ-℃紧凑率，并且获得了与Δ-℃连续性和Δ-℃紧凑性相关的一些定理。 还讨论了一些其他类型的连续性，并获得了有趣的结果。
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