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Convex meromorphic mappings

100%

Livingston A.

Annales Polonici Mathematici

1994

tom 59

nr 3

275-291

We study functions f(z) which are meromorphic and univalent in the unit disk with a simple pole at z = p, 0 < p < 1, and which map the unit disk onto a domain whose complement is either convex or is starlike with respect to a point w₀ ≠ 0.

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Harmonic mappings in the exterior of the unit disk

88%

Gregorczyk M., Widomski J.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2010

tom 64

nr 1

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition\(\sum_{n=1}^{\infty}n^{p}(|a_{n}|+|b_{n}|)\leq 1\). We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Gregorczyk M.

1 Livingston A.

1 Widomski J.

1 2010

1 1994

Wyniki wyszukiwania

Convex meromorphic mappings

Harmonic mappings in the exterior of the unit disk