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

9 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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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.\}",

note = "Publisher Copyright: {\textcopyright} 2017 Australian Mathematical Publishing Association Inc.",

year = "2017",

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AU - Ferrada-Salas, Álvaro

AU - Hernández, Rodrigo

AU - Martín, María J.

PY - 2017/10/1

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.

KW - convex combinations

KW - convex harmonic mappings

UR - https://www.scopus.com/pages/publications/85026900736

U2 - 10.1017/S0004972717000685

DO - 10.1017/S0004972717000685

M3 - Article

AN - SCOPUS:85026900736

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VL - 96

SP - 256

EP - 262

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

ON CONVEX COMBINATIONS of CONVEX HARMONIC MAPPINGS

Abstract

Keywords

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