A Distortion Theorem for Analytic Functions
نویسندگان
چکیده
منابع مشابه
A Fixed Point Theorem for Analytic Functions
We denote that set by A(z,w,k) and (following [1]) call it the Apollonius circle of constant k associated to the points z and w. The set A(z,w,k) is a circle for all values of k other than 1 when it is a line. In this paper, we consider z,w ∈ U, show that if z = w, then necessarily A(z,w, √ (1−|w|2)/(1−|z|2)) meets the unit circle twice, consider the arc on the unit circle with those endpoints,...
متن کاملDistortion Theorems for a Special Class of Analytic Functions
Sharp bounds are derived for the derivative of analytic functions of class .P,, defined by the condition |/>(z) —l/2a|<: l/2a, O^a^l, p(f>) = \. These results are improved for the class of functions with missing terms. Application is made to the class of functions with derivative G Px and the radius of convexity is determined for this class.
متن کاملTitchmarsh theorem for Jacobi Dini-Lipshitz functions
Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...
متن کاملFluctuations for Analytic Test Functions in the Single Ring Theorem
We consider a non-Hermitian random matrix A whose distribution is invariant under the left and right actions of the unitary group. The so-called Single Ring Theorem, proved by Guionnet, Krishnapur and Zeitouni [31], states that the empirical eigenvalue distribution of A converges to a limit measure supported by an annulus S. In this text, we establish the convergence in distribution of random v...
متن کاملA Subclass of Analytic Functions Associated with Hypergeometric Functions
In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.2307/2038009