International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 443-454
doi:10.1155/S016117128400048X
A unified approach to radius of convexity problems for certain classes of univalent analytic functions
1School of Mathematical Sciences, University of Khartoum, P.O. Box 321, Khartoum, Sudan
2Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India
Received 30 April 1982
Copyright © 1984 M. L. Mogra and O. P. Juneja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider functions f analytic in the unit disc and assume the power series representation of the form f(z)=z+an+1zn+1+an+2zn+2+… where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier estimates concerning the radius of convexity such as those involving fixed second coefficient, n initial gaps, n+1 symmetric gaps, etc. are discussed. It is shown that several known results, follow as special cases of those presented in this paper.