The radius of convexity of certain analytic functions II

J. S. Ratti

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-7

Abstract:

In [2], MacGregor found the radius of convexity of the functions f ( z ) = z + a 2 z 2 + a 3 z 3 + … , analytic and univalent such that | f ′ ( z ) − 1 | < 1 . This paper generalized MacGregor's theorem, by considering another univalent function g ( z ) = z + b 2 z 2 + b 3 z 3 + … such that | f ′ ( z ) g ′ ( z ) − 1 | < 1 for | z | < 1 . Several theorems are proved with sharp results for the radius of convexity of the subfamilies of functions associated with the cases: g ( z ) is starlike for | z | < 1 , g ( z ) is convex for | z | < 1 , Re { g ′ ( z ) } > α ( α = 0 , 1 / 2 ) .

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:180890

DOI: 10.1155/S0161171280000361

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