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In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function f is Abel statistically continuous on a subset E of R, the set of real numbers, if it preserves Abel statistical convergent sequences, i.e. (f (p k )) is Abel statistically convergent whenever (p k ) is an Abel statistical convergent sequence of points in E, where a sequence (p k ) of point in R is called Abel statistically convergent to a real number L if Abel density of the set {k ∈ N 0 : |p k − L| ≥ ε} is 0 for every ε > 0. Some other types of continuities are also studied and interesting results are obtained.

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