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Functions of bounded boundary rotation. (English) Zbl 0224.30024

MSC:
30C45Special classes of univalent and multivalent functions
References:
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[2]Mark Finkelstein,On the relation between measures and convex analytic functions, Illinois J. Math.12 (1968), 175–183.
[3]V. Paatero,Über die Konforme Abbildungen von Gebeiten deren Ränder von beschränkter Drehung sind, Ann. Acad. Sci. Fenn. Ser. A 33 (1933), No. 9.
[4]Bernard Pinchuk,A variational method for functions of bounded boundary rotation, Trans. Amer. Math. Soc.138 (1969), 107–113. · doi:10.1090/S0002-9947-1969-0237761-8
[5]Christian Pommerenke,Linear-invariente Familien analytischer Funktionen I, Math. Ann.155 (1964), 108–154. · Zbl 0128.30105 · doi:10.1007/BF01344077
[6]M. S. Robertson,Radii of star-likeness and close-to-convexity, Proc. Amer. Math. Soc.16 (1965), 847–852.
[7]M. S. Robertson,Coefficients of functions with bounded boundary rotation, Canad. J. Math.21 (1969), 1477–1482. · Zbl 0188.38203 · doi:10.4153/CJM-1969-161-2
[8]M. S. Robertson,Univalent functions f(z) for which zf’(z) is spirallike, Michigan Math. J.16 (1969), 97–101. · Zbl 0175.36602 · doi:10.1307/mmj/1029000208
[9]W. C. Royster,On the univalence of a certain integral, Michigan Math. J.12 (1965), 385–387. · Zbl 0193.37301 · doi:10.1307/mmj/1028999421
[10]A. Schild,On a class of univalent starshaped mappings, Proc. Amer. Math. Soc.9 (1958) 751–757. · doi:10.1090/S0002-9939-1958-0095954-5
[11]Ted J. Suffridge,Convolutions of convex functions, J. Math. Mech.15 (1966), 795–804.