International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 319-324
doi:10.1155/S0161171202007895
Sufficient conditions for starlikeness associated with parabolic region
V. Ravichandran1
, A. Gangadharan1
and T.N. Shanmugam3
1Department of Mathematics and Computer Applications, Sri Venkateswara College of Engineering, Sriperumbudur 602 105, India
3Department of Mathematics, Anna University, Madras 600 025, India
Abstract
An analytic function f(z)=z+a n+1 z n+1+⋯, defined on the unit disk △={z:|z|<1}, is in the class S p if z f′(z)/f(z) is in the parabolic region Rew>|w−1|. This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in S p are obtained. In particular, we find condition on λ such that the function f(z), satisfying (1−α)(f(z)/z) μ+αf′(z)(f(z)/z) μ−1≺1+λz, is in S p.