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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the univalence of a certain integral


Authors: E. P. Merkes and D. J. Wright
Journal: Proc. Amer. Math. Soc. 27 (1971), 97-100
MSC: Primary 30.42
MathSciNet review: 0269825
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Abstract: We consider the function $ g(z) = \smallint _0^z{[f(t)/t]^\alpha }dt$ for $ f$ in the classes of convex, starlike, and close-to-convex univalent functions, and we determine precisely which values of $ \alpha $ yield a close-to-convex function $ g$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0269825-1
PII: S 0002-9939(1971)0269825-1
Keywords: Univalent function, starlike, convex, close-to-convex
Article copyright: © Copyright 1971 American Mathematical Society