Directional Convexity of Combinations of Harmonic Half-Plane and Strip Mappings
Commun. Korean Math. Soc.
Published online May 13, 2021
Subzar Beig and Vaithiyanathan Ravichandran
Government Degree College Uri, Baramulla--193 123, Jammu and Kashmir; NATIONAL INSTITUTE OF TECHNOLOGY TIRUCHIRAPPALLI
Abstract : For k = 1, 2, let fk = hk + gk be normalized harmonic right half-planeor vertical strip mappings. We consider the convex combination ˆf = ηf1 + (1 − η)f2 = ηh1+(1−η)h2+ηg1 + (1 − η)g2 and the combination ˜f = ηh1+(1−η)h2+ηg1 + (1 − η)g2. For real η, the two mappings ˆf and ˜f are the same. We investigate the univalence and directional convexity of ˆf and ˜f for η ∈ C. Some sufficient conditions are found for convexity of the combination ˜f.
Keywords : harmonic mappings; directional convexity; harmonic shear; linear combination; strip mappings
MSC numbers : 31A05; 30C45
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd