ABSTRACT
We remark that (A-9) shows not only that f is convex, but that f is convex of order a = 0.228 · · · . The radius of convexity of f is not known. Recently I. Serb in [ 381 ] obtained the radius of convexity of the function 1/ f. [See the discussion involving condition (5.2-14).]
Proof From (A-10) we obtain ,
where
- 1,
Re - = Re / 2 ~ 1. g(z) (e-z+z-1)z This can be rewritten in the equivalent form:
(A-12) I e-z + z-1 - .!.I z2 2
and this inequality holds if and only if
r r2 r3 1 +-+-+··· <-3! 4! 5! - 2.
