Convex and alpha-prestarlike subordination chains |
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Authors: | Gabriela Kohr Petru T Mocanu |
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Institution: | Faculty of Mathematics and Computer Science, Babe?-Bolyai University, 1 M. Kog?lniceanu street, 400084 Cluj-Napoca, Romania |
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Abstract: | In this paper we consider convex subordination chains (c.s.c.) and alpha-prestarlike subordination chains (α-p.s.c.) over (0,1] on the unit disc in the complex plane. We obtain sufficient conditions for a mapping f(z,t) to be an α-p.s.c. over (0,1], which generalize a well-known result of Ruscheweyh St. Ruscheweyh, Convolutions in Geometric Function Theory, Les Presses de l'Université de Montreal, 1982]. We also obtain sufficient conditions for injectivity for nonanalytic mappings on the unit disc, and give certain examples of α-c.s.c. over (0,1] on the unit disc. |
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Keywords: | Convex function Convex subordination chain α-Prestarlike subordination chain Univalent function Univalent subordination chain |
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