Abstract
A class of functions $\mathcal {A}$ is defined which contains the spirallike and close-to-convex functions. By decomposing $\mathcal {A}$ into subclasses in a natural way, some basic properties of $\mathcal {A}$ and these subclasses are determined, including solutions to extremal problems; distortion theorems; coefficient inequalities; and the radii of convexity and close-to-convexity.
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