AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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Authors: MARTIN CHUAQUI, BRAD OSGOOD.
DOI: 10.24193/subbmath. 2022.2.17
Published Online: 2022-06-10
Published Print: 2022-06-30
pp. 431-440
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Abstract: 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 convo- lution between C and S, as well as correspondences between the subclasses of convex and starlike mappings that have n-fold symmetry.
Key words: Convolution, convex mapping, starlike mapping, convex polygon, slit mapping, Polya-Schoenberg conjecture.
Mathematics Subject Classification (2010): 30C45, 30C30.
