Convolutions of harmonic right half-plane mappings
نویسندگان
چکیده
منابع مشابه
On the Linear Combinations of Slanted Half-Plane Harmonic Mappings
In this paper, the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.
متن کاملConvolutions of Harmonic Convex Mappings
The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right halfplane mapping or a normalized vertical strip mapping is convex in the direction of the real axis. provided that it is locally univalent. In this paper, we prove that in general the assumption of local univalency cannot be omitted. However, we are able to show t...
متن کاملConvolutions of Planar Harmonic Convex Mappings
Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...
متن کاملHarmonic Mappings in the Plane
A catalog record for this book is available from the British Library. Harmonic mappings in the plane / Peter Duren. Includes bibliographical references and index.
متن کاملQuasiconformal Extension of Harmonic Mappings in the Plane
Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane. Introduction A well-known criterion due to Becker [5] states that if a locally univalent analytic function φ in the unit disk D satisfies (1) sup z∈D ∣∣∣∣φ′′(z) φ′(z) ∣∣∣∣ (1− ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Open Mathematics
سال: 2016
ISSN: 2391-5455
DOI: 10.1515/math-2016-0069