Padmanabhan, K. S.; Manjini, R. Certain applications of differential subordination. (English) Zbl 0608.30013 Publ. Inst. Math., Nouv. Sér. 39(53), 107-118 (1986). Let A denote the class of functions f that are regular in the unit disk E with \(f(0)=0=f'(0)-1\). For real a let \(k_ a(z)=z/(1-z)^ a\) and let h be a regular convex univalent function with \(h(0)=1\) and \(Re[h(z)]>0\) in E. The authors define classes \(K_ a(h)\) to be the set of \(f\in A\) such that \(1+z(k_ a*f)'(z)/(k_ a*f)(z)\) is subordinate to h in E. Various properties of \(K_ a(h)\) and certain related classes are studied. These classes generalize various subclasses of A such as the class of \(\alpha\)- convex functions. See, for example, S. S. Miller, P. T. Mocanu and M. O. Reade [Rev. Roum. Math. Pures Appl. 19, 213-224 (1974; Zbl 0278.30011)]. Reviewer: D.V.V.Wend Cited in 7 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination Keywords:subordinate; \(\alpha \)-convex functions Citations:Zbl 0278.30011 PDFBibTeX XMLCite \textit{K. S. Padmanabhan} and \textit{R. Manjini}, Publ. Inst. Math., Nouv. Sér. 39(53), 107--118 (1986; Zbl 0608.30013) Full Text: EuDML