منابع مشابه
Coefficients of Univalent Functions
The interplay of geometry and analysis is perhaps the most fascinating aspect of complex function theory. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior. A function is said to be univalent (or schlichi) if it never takes the same value twice: f(z{) # f(z2) if zx #= z2. The present survey will focus upon the class S ...
متن کاملBounds for the Coefficients of Univalent Functions
assumed regular and Univalent in \z\ <1, in terms of the domain onto which \z\ <1 is mapped through (1). A typical result, cf. (27), is that if this domain does not cover arbitrarily large circles, then1 a„ = 0(log n). Let W be the domain in the w-plane onto which \z\ <1 is mapped through (1) and denote by .4(72) the radius of the largest circle with center on |w| = 72 the whole interior of whi...
متن کاملOn Nonvanishing Univalent Functions with Real Coefficients*
S O u {1} is a compact subset of A. Duren and Schober had been interested in extreme points and support points of S o. Recall that a support point of a family F is a function which maximizes the real part of some continuous linear functional, that is not constant over F. We shall give a characterization of the extreme points and support points of the subfamily So(R ) of nonvanishing univalent f...
متن کاملSub-riemannian Geometry of the Coefficients of Univalent Functions
We consider coefficient bodies Mn for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov’s operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie-Poisson bracket they form a grading of subspaces with the first subspace a...
متن کاملOn Subclass of Analytic Univalent Functions Associated with Negative Coefficients
M. H. Al-Abbadi and M. Darus 2009 recently introduced a new generalized derivative operator μ λ1 ,λ2 , which generalizedmany well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit disk U {z ∈ C : |z| < 1} which is defined by new generalized derivative operator. Some results on coefficient ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1977
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1977-14324-3