Obradović, Milutin Simple sufficient conditions for univalence. (English) Zbl 0992.30005 Mat. Vesn. 49, No. 3-4, 241-244 (1997). As usual, let \(A\) denote the class of functions \(f\) analytic in the unit disc \(U=\{z:|z|< 1 \}\) with \(f(0)=f'(0)-1=0\).The author proves: a) if \(f \in A\) and \(f^{\prime\prime }(z) \leq 1\), \(z \in U\), then \(f\) is starlike; b) if \(f \in A\) and \(f^{\prime\prime }(z) \leq {{1}\over {2}}\), \(z \in U\), then \(f\) is convex. Reviewer: Miroljub Jevtić (Beograd) Cited in 14 Documents MSC: 30C55 General theory of univalent and multivalent functions of one complex variable Keywords:convex and starlike functions; subordinate PDFBibTeX XMLCite \textit{M. Obradović}, Mat. Vesn. 49, No. 3--4, 241--244 (1997; Zbl 0992.30005) Full Text: EuDML