Convex and alpha-prestarlike subordination chains

Abstract: In this paper we consider convex subordination chains (c.s.c.) and alpha-prestarlike subordination chains (α-p.s.c.) over on the unit disc in the complex plane. We obtain sufficient conditions for a mapping to be an α-p.s.c. over , 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 on the unit disc. [Copyright &y& Elsevier]