Univalent and Starlike Generalized Hypergeometric Functions

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 ( z 1 ) = f ( z 2 ) for implies that z 1 = z 2 . A set is said to be starlike with respect to the line segment joining w 0 to every other point lies entirely in . If a function f(z) maps onto a domain that is starlike with respect to w 0 , then f(z) is said to be starlike with respect to w 0 . In particular, if w 0 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 .