Document Type
Article
Publication Date
1980
Digital Object Identifier (DOI)
https://doi.org/10.1155/S0161171280000361
Abstract
In [2], MacGregor found the radius of convexity of the functions f(z)=z+a2z2+a3z3+…, analytic and univalent such that |f′(z)−1|<1. This paper generalized MacGregor's theorem, by considering another univalent function g(z)=z+b2z2+b3z3+… 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).
Rights Information
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
International Journal of Mathematics and Mathematical Sciences, v. 3, art. 180890
Scholar Commons Citation
Ratti, J. S., "The Radius of Convexity of Certain Analytic Functions II" (1980). Mathematics and Statistics Faculty Publications. 82.
https://digitalcommons.usf.edu/mth_facpub/82
