Distortions properties of alpha-starlike functions
نویسندگان
چکیده
منابع مشابه
The Study Properties of Subclass of Starlike Functions
In this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk U.Such results as coecientinequalities. The results presented here would provide extensions of those givenin earlier works.
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We determine the order of convexity of hypergeometric functions z 7→ F (a, b, c, z) as well as the order of starlikeness of shifted hypergeometric functions z 7→ zF (a, b, c, z), for certain ranges of the real parameters a, b and c. As a consequence we obtain the sharp lower bound for the order of convexity of the convolution (f ∗ g)(z) := ∑∞ n=0 anbnz n when f(z) = ∑∞ n=0 anz n is convex of or...
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The purpose of the present paper is to give some characterizations for a Gaussian hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.
متن کاملthe study properties of subclass of starlike functions
in this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk u.such results as coecientinequalities. the results presented here would provide extensions of those givenin earlier works.
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: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0310222-x