On an extension of Ozaki’s condition
Abstract It is known that if {f(z)=z^{p}+\sum_{n=p+1}^{\infty}a_{n}z^{n}} and it is analytic in a convex domain {D\subset\mathbb{C}} and, for some real α, we have {\operatorname{\mathfrak{Re}}\{\exp(i\alpha)f^{(p)}(z)\}>0} , {z\in D} , then {f(z)} is at most p-valent in D. This Ozaki condition is a generalization of the well-known Noshiro–Warschawski univalence condition. In this paper, we consider the radius of univalence of functions {g(z)=z+\sum_{n=1}^{\infty}b_{n}z^{n}} such that {g^{\prime}(z)\prec[(1+z)^{2}/(1-z)^{2}]} and some related problems.
2010 ◽
Vol 259
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pp. 1230-1247
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1991 ◽
Vol 117
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pp. 21-29
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2011 ◽
Vol 29
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pp. 523-549
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2009 ◽
Vol 159
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pp. 104-112
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2018 ◽
Vol 300
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pp. 72-87
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