Results 61 to 70 of about 1,183 (204)

Two-point distortion theorems for univalent functions [PDF]

Pacific Journal of Mathematics, 1994
The authors establish a one-parameter family of symmetric, linearly invariant two-point distortion theorems for univalent functions defined on the unit disk. The weakest theorem in the family is a symmetric, linearly invariant form of a classical distortion theorem of Koebe, while another special case is a distortion theorem of \textit{Ch.
Kim, Seong-A., Minda, David
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On a subclass of Bazilevič functions

International Journal of Mathematics and Mathematical Sciences, 1985
Let B(α) be the class of normalised Bazilevič functions of type α>0 with respect to the starlike function g. Let B1(α) be the subclass of B(α) when g(z)≡z. Distortion theorems and coefficient estimates are obtained for functions belonging to B1(α).
D. K. Thomas
doaj   +1 more source

TWO-POINT DISTORTION THEOREMS FOR HARMONIC MAPPINGS

, 2009
In earlier work, the authors have extended Nehari's well-known Schwarzian derivative criterion for univalence of analytic functions to a univalence criterion for canonical lifts of harmonic mappings to minimal surfaces.
Duren, Peter, Osgood, Brad, Chuaqui, Martin   +2 more
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Distortion theorems for rational functions without poles or zeros in simply connected domains

, 2000
We prove distortion theorems for rational functions without poles or zeros in simply connected domains. The distance between the values u(z 1) and u(z 2) assumed by such a rational function is limited by its degree and by the hyperbolic distance between ...
Blondel, Vincent, Rupp, Rainer
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A distortion theorem for quasiconformal mappings [PDF]

Bulletin de la Société mathématique de France, 1986
There exists a constant \(C=C(K,n)\) such that for any K-quasiconformal mapping \(f: B^ n\to {\mathbb{R}}^ n\) and for any \(z\in B\) there exists \(x\in \partial B^ n\) with \(| z-x| 1) \] where \(f^*\) is the nontangential maximal function.
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MULTIVALENT α - CONVEX HARMONIC MAPPINGS

Проблемы анализа, 2002
In this paper we give coefficient conditions for complex-valued harmonic functions that are ultivalent, sense-preserving and α-convex. We determine the extreme points, distortion and covering theorems for these mappings.
GANCZAR A.
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Some theorems on boundary distortion [PDF]

Transactions of the American Mathematical Society, 1956
one. 2. Our method of treating these results is in all cases what may be called the method of the extremal metric. It is essentially the method used to such advantage by Gr6tzsch, however we use the more convenient formulation due to Ahlfors and Beurling.
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Some Distortion Theorems for Starlike Harmonic Functions [PDF]

, 2010
MSC 2010: 30C55, 30C45Distortion and growth theorems are ...
Yavuz Duman, Emel
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An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions

International Journal of Differential Equations, 2009
Let 𝒜 be the class of analytic functions in the open unit disk . We define Θα,β:𝒜→𝒜 by (Θα,βf)(z):=Γ(2−α)zαDzα(Γ(2−β)zβDzβf(z)),(α,β≠2,3,4…), where Dzγf is the fractional derivative of f of order γ. If α,β∈[0,1], then a function f
Oqlah Al-Refai, Maslina Darus
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A distortion theorem for analytic functions [PDF]

Proceedings of the American Mathematical Society, 1971
Let f ( z ) f(z) be a function analytic in the disk E { z : | z | > 1 } E\{ z:|z| > 1\} and for some real number n > 0 n > 0 let
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