Radius of starlikeness through subordination
DOI:
https://doi.org/10.24193/subbmath.2023.1.12Keywords:
Univalent functions, convex functions, starlike functions, subordination, radius of starlikeness.Abstract
A normalized function f on the open unit disc is starlike (or convex) univalent if the associated function zf/(z)/f (z) (or 1+zf//(z)/f/(z)) is a function with positive real part. The radius of starlikeness or convexity is usually obtained by using the estimates for functions with positive real part. Using subordination, we examine the radius of various starlikeness, in particular, radii of Janowski starlikeness and starlikeness of order β, for the function f when the function f is either convex or (zf/(z) + αz²f//(z))/f (z) lies in the right-half plane. Radii of starlikeness associated with lemniscate of Bernoulli and exponential functions are also considered.
Mathematics Subject Classification (2010): 30C80, 30C45.
Received 21 February 2020; Revised 09 March 2020. Published Online: 2023-03-20. Published Print: 2023-04-30
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