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Starlikeness for Certain Close-to-Star Functions

By R. Kanaga and Vaishnavi Ravichandran
We find the radius of starlikeness of order \(\alpha\), \(0\leq \alpha<1\), of normalized analytic functions \(f\) on the unit disk satisfying either \(\operatorname{Re}(f(z)/g(z))>0\) or \(\left| (f(z)/g(z))-1\right|<1\) for some close-to-star function \(g\) with \(\operatorname{Re}(g(z)/(z+z^2/2))>0\) as well as of the class of close-to-star functions \(f\) satisfying \(\operatorname{Re}(f(z)/(z+z^2/2))>0\). Several other radii such as... Show more
March 12, 2020
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Starlikeness for Certain Close-to-Star Functions
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