Singh, Sukhjit; Gupta, Sushma Some applications of a first order differential subordination. (English) Zbl 1083.30016 JIPAM, J. Inequal. Pure Appl. Math. 5, No. 3, Paper No. 78, 15 p. (2004). Let \(p\) and \(q\) be analytic functions in the unit disc \(E={z:| z| <1}\), with \(p(0)=q(0)=1\). Assume that \(\alpha\) and \(\delta\) are real numbers such that \(0<\delta\leq 1\), \(\alpha+\delta\geq 0\). Let \(\beta\) and \(\gamma\) be complex numbers with \(\beta\neq 0\). The authors investigate the differential subordination \[ p^{\alpha}(z)\left(p(z)+\dfrac{zp'(z)}{\beta p(z)+\gamma}\right)^{\delta}\prec q^{\alpha}(z)\left(q(z)+\dfrac{zq'(z)}{\beta q(z)+\gamma}\right)^{\delta} \] for \(z\in E\), and obtained several sufficient conditions for starlikeness and univalence of functions analytic in the unit disc \(E\). Reviewer: Maslina Darus (Selangor) Cited in 1 Document MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C50 Coefficient problems for univalent and multivalent functions of one complex variable Keywords:univalent function; starlike function; convex function; differential subordination PDF BibTeX XML Cite \textit{S. Singh} and \textit{S. Gupta}, JIPAM, J. Inequal. Pure Appl. Math. 5, No. 3, Paper No. 78, 15 p. (2004; Zbl 1083.30016) Full Text: EuDML OpenURL