Displaying similar documents to “Univalent harmonic mappings”

Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle

Tetsuo Inoue (1992)

Annales Polonici Mathematici

Similarity:

Let f(z) be a conformal mapping of an annulus A(R) = 1 < |z| < R and let f(A(R)) be a ring domain bounded by a circle and a k-circle. If R(φ) = w : arg w = φ, and l(φ) - 1 is the linear measure of f(A(R)) ∩ R(φ), then we determine the sharp lower bound of l ( φ 1 ) + l ( φ 2 ) for fixed φ 1 and φ 2 ( 0 ≤ φ 1 ≤ φ 2 ≤ 2 π ) .

Extreme points of subordination and weak subordination families of harmonic mappings

Jinjing Qiao, Xiantao Wang (2011)

Czechoslovak Mathematical Journal

Similarity:

The aim of the paper is to discuss the extreme points of subordination and weak subordination families of harmonic mappings. Several necessary conditions and sufficient conditions for harmonic mappings to be extreme points of the corresponding families are established.

Univalent harmonic mappings II

Albert E. Livingston (1997)

Annales Polonici Mathematici

Similarity:

Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= z: |z| < 1. We consider the class S H ( U , Ω ( a , b ) ) of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, f z ( 0 ) > 0 and f z ̅ ( 0 ) = 0 .

On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

Agnieszka Sibelska (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ . In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998–2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazinska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri...