ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS

Álvaro Ferrada-Salas; Rodrigo Hernández; María J. Martín

doi:10.1017/S0004972717000685

ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS

Álvaro Ferrada-Salas, Rodrigo Hernández, María J. Martín

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The family F_λ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in F_λ are convex.

Original language	English
Pages (from-to)	256-262
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	96
Issue number	2
DOIs	https://doi.org/10.1017/S0004972717000685
State	Published - 1 Oct 2017

Keywords

convex combinations
convex harmonic mappings

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10.1017/S0004972717000685

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title = "ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS",

abstract = "The family Fλ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in Fλ are convex.",

keywords = "convex combinations, convex harmonic mappings",

author = "{\'A}lvaro Ferrada-Salas and Rodrigo Hern{\'a}ndez and Mart{\'i}n, {Mar{\'i}a J.}",

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AU - Martín, María J.

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Y1 - 2017/10/1

N2 - The family Fλ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in Fλ are convex.

AB - The family Fλ of orientation-preserving harmonic functions f = h+g in the unit disc (normalised in the standard way) satisfying {equation presented} for some {equation presented} , along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in Fλ are convex.

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KW - convex harmonic mappings

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JF - Bulletin of the Australian Mathematical Society

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ER -

ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS

Abstract

Keywords

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