Radius of starlikeness through subordination

Asha Sebastian, Vaithiyanathan Ravichandran


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 beta, for the function f when the function f is either convex or  \((zf'(z)+\alpha z^2f''(z))/f(z)\) lies in the right-half plane. Radii of starlikeness associated with lemniscate of Bernoulli and exponential functions are also considered.


univalent functions; convex functions; starlike functions; subordination; radius of starlikeness

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DOI: http://dx.doi.org/10.24193/subbmath.2023.1.12


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