Hull subordination and extremal problems for starlike and spirallike mappings
نویسندگان
چکیده
منابع مشابه
Extremal Problems for Star Mappings
The results obtained in §§1-2 are applied in §3 to show that the maximum possible value of dt{B log/'(z) + C log [/(z)/z]} at a point Zo of the unit circle, for the class of functions f(z) =z+ • • • which map |z| <1 conformally onto star-shaped regions, is attained for a function w=f(z) which maps the unit circle onto the w-plane with one or two radial slits. In §§4-5, we decide between these t...
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We prove a subordination relation for a subclass of the class of λ-spirallike functions.
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In an earlier paper [l] the writer showed the development of a variational method for starlike functions and applied this method to a general class of extremal problems connected with the coefficients of the function. It is the purpose of this paper to study the classes of extremal problems to which this variational method can be applied and to make some remarks as to its utility. The class S* ...
متن کاملApplications of subordination theory to starlike functions
Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1973-0338339-9