Injectivity and Starlikeness of Sections of a Class of Univalent Functions
نویسندگان
چکیده
For r > 0, let Dr := {z ∈ C : |z| < r} and D := D1 be the open unit disk in the complex plane C. Let A denote the family of all functions f that are analytic in D with the normalization f(0) = 0 = f ′(0) − 1. Let S denote the class of functions in A that are univalent in D. A domain D in C is called starlike (with respect to the origin) if every line segment joining the origin to any other point in D lies completely inside D. A function f ∈ S is called starlike if f(D) is a starlike domain. The class of all starlike functions is denoted by S∗, and functions f ∈ S∗ are characterized by the condition
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