On the Fourth Coefficient of the Inverse of a Starlike Function of Positive Order
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We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.
2005 ◽
Vol 2005
(4)
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pp. 561-570
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2019 ◽
Vol 73
(1)
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pp. 49
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1981 ◽
Vol 33
(5)
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pp. 1255-1260
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1995 ◽
Vol 47
(6)
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pp. 1121-1147
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