Displaying similar documents to “Harmonic mappings in the exterior of the unit disk”

Harmonic mappings in the exterior of the unit disk

Magdalena Gregorczyk, Jarosław Widomski (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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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 ∑ n = 1 ∞ n p ( | a n | + | b n | ) ≤ 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.

Fully starlike and fully convex harmonic mappings of order α

Sumit Nagpal, V. Ravichandran (2013)

Annales Polonici Mathematici

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The hereditary properties of convexity and starlikeness for conformal mappings do not generalize to univalent harmonic mappings. This failure leads to the notions of fully starlike and fully convex mappings. In this paper, properties of fully starlike mappings of order α and fully convex mappings of order α (0 ≤ α < 1) are studied; in particular, the bounds for the radius of full starlikeness of order α as well as the radius of full convexity of order α are determined for certain...

Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings

David Kalaj (2011)

Studia Mathematica

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We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.

On Dyakonov type theorems for harmonic quasiregular mappings

Miloš Arsenović, Miroslav Pavlović (2017)

Czechoslovak Mathematical Journal

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We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.

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

Agnieszka Sibelska (2010)

Annales UMCS, Mathematica

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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. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri...