Convexity of some particular functions. (English) Zbl 0548.30006

Mocanu, Petru T.

Stud. Univ. Babeș-Bolyai, Math. 29, 70-73 (1984).

The author shows that f and log f are both convex in the unit disk, when \(f(z)=z(\exp z-1)^{-1}\). His proofs are based on lemmas he derives from the work of D. R. Wilken and J. Feng [J. Lond. Math. Soc., II. Ser. 21, 287-290 (1980; Zbl 0431.30007)]; E. P. Merkes and D. J. Wright [Proc. Am. Math. Soc. 27, 97-100 (1971; Zbl 0221.30012)]; and the reviewer [Proc. Am. Math. Soc. 16, 755-758 (1965; Zbl 0158.077)].

Reviewer: R.Libera

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

convex function

Citations:

Zbl 0431.30007; Zbl 0221.30012; Zbl 0158.077