Coefficients of symmetric functions of bounded boundary rotation

Koepf, Wolfram

doi:10.1090/S0002-9939-1989-0930244-7

Coefficients of symmetric functions of bounded boundary rotation
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Proc. Amer. Math. Soc. 105 (1989), 324-329 Request permission

Abstract:

The well-known inclusion relation between functions with bounded boundary rotation and close-to-convex functions of some order is extended to $m$-fold symmetric functions. This leads solving the corresponding result for close-to-convex functions to the sharp coefficient bounds for $m$-fold symmetric functions of bounded boundary rotation at most $k\pi$ when $k \geq 2m$. Moreover it shows that an $m$-fold symmetric function of bounded boundary rotation at most $(2m + 2)\pi$ is close-to-convex and thus univalent.

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Über die konforme Abbildung von Gebieten deren Ränder von beschränkter Drehung sind

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