The Class of Functions Convex in the Negative Direction of the Imaginary Axis of Order (α,β)
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Mapping Properties of Hypergeometric Functions and Convolutions of Starlike or Convex Functions of Order alpha
We determine the order of convexity of hypergeometric functions z 7→ F (a, b, c, z) as well as the order of starlikeness of shifted hypergeometric functions z 7→ zF (a, b, c, z), for certain ranges of the real parameters a, b and c. As a consequence we obtain the sharp lower bound for the order of convexity of the convolution (f ∗ g)(z) := ∑∞ n=0 anbnz n when f(z) = ∑∞ n=0 anz n is convex of or...
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