starlike region

starlike region

[′stär‚līk ‚rē·jən]
(mathematics)
A region in the complex number plane such that the line segment joining any of its points to the origin lies entirely in the region.
References in periodicals archive ?
Consider again the starlike region using (2.5) of Example 2.1, but now with a = 3.
A region [ohm] from the complex plane C is called convex if for every two points [[omega].sub.1], [[omega].sub.2] [member of] [ohm] the closed line segment [[omega].sub.1], [[omega].sub.2] = {(1 - t)[[omega].sub.1] + [t[omega].sub.2]: 0 [less than or equal to] t [less than or equal to] 1} lies in [ohm] Fixing [[omega].sub.1] = 0 brings the definition of starlike region. If A denotes the class of functions f(z) that are analytic in the unit disk u = {z: |z| < 1} and normalized by f(0) = f'(0) - 1 = 0, then a function f [member of] A is called convex or starlike if it maps u into a convex or starlike region, respectively.