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Published online by Cambridge University Press: 20 November 2018
A single-valued function f(z) is said to be univalent in a domain if it never takes on the same value twice, that is, if f(z1) = f(z2) for
implies that z1 = z2. A set
is said to be starlike with respect to
the line segment joining w0 to every other point
lies entirely in
. If a function f(z) maps
onto a domain that is starlike with respect to w0, then f(z) is said to be starlike with respect to w0. In particular, if w0 is the origin, then we say that f(z) is a starlike function. Further, a set
is said to be convex if the line segment joining any two points of
lies entirely in
. If a function f(z) maps
onto a convex domain, then we say that f(z) is a convex function in
.