Generating Starlike and Convex Univalent Functions

نویسندگان

  • Vanessa Bertoni
  • Dimitar K. Dimitrov
  • V. Bertoni
  • D. K. Dimitrov
چکیده

Alexander [1] was the first to introduce certain subclasses of univalent functions examining the geometric properties of the image f(D) of D under f . The convex functions are those that map D onto a convex set. A function w = f(z) is said to be starlike if, together with any of its points w, the image f(D) contains the entire segment {tw : 0 ≤ t ≤ 1}. Thus we introduce the denotations S = {f ∈ S : f is starlike in D}, K = {f ∈ S : f is convex in D}.

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تاریخ انتشار 2007