On convolution, convex, and starlike mappings - CHUAQUI, Martin; OSGOOD, Brad (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
Let C and S∗ stand for the classes of convex and starlike mapping in D, and let co(C), co(S∗) denote the closures of the respective convex hulls. We derive characterizations for when the convolution of mappings in co(C) is convex, as well as when the convolution of mappings in co(S∗) is starlike. Several characterizations in terms of convolution are given for convexity within co(C) and for starlikeness within co(S∗). We also obtain a correspondence via convolution between C and S∗, as well as correspondences between the subclasses of convex and starlike mappings that have n-fold symmetry. Mathematics Subject Classification (2010): 30C45, 30C30. Received 19 January 2022; Accepted 20 January.