Radius problems for starlike functions associated with the sine function
Bulletin of the Iranian Mathematical Society, 2019•Springer
Let S^* _s S s∗ be the class of normalized analytic functions f defined on the unit disk such
that the quantity zf'(z)/f (z) zf′(z)/f (z) lies in an eight-shaped region in the right-half plane,
which is the image of the unit disk under an entire function defined by φ (z)= 1+\sin z φ (z)=
1+ sin z. For this class, we determine the S^* _s S s∗-radii for the class of Janowski starlike
functions and some other geometrically defined classes. A relation between this class and
the class of Janowski starlike functions is also discussed.
that the quantity zf'(z)/f (z) zf′(z)/f (z) lies in an eight-shaped region in the right-half plane,
which is the image of the unit disk under an entire function defined by φ (z)= 1+\sin z φ (z)=
1+ sin z. For this class, we determine the S^* _s S s∗-radii for the class of Janowski starlike
functions and some other geometrically defined classes. A relation between this class and
the class of Janowski starlike functions is also discussed.
Abstract
Let be the class of normalized analytic functions f defined on the unit disk such that the quantity lies in an eight-shaped region in the right-half plane, which is the image of the unit disk under an entire function defined by . For this class, we determine the -radii for the class of Janowski starlike functions and some other geometrically defined classes. A relation between this class and the class of Janowski starlike functions is also discussed.
Springer
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