A convolution property of univalent harmonic right half-plane mappings

Authors

Md Firoz Ali, National Institute of Technology, Durgapur
Vasudevarao Allu, Indian Institute of Technology Bhubaneswar
Nirupam Ghosh, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Monatshefte fur Mathematik

Abstract

We consider the convolution of right half-plane harmonic mappings in the unit disk D:={z∈C:|z|<1} with respective dilatations eiα(z+ a) / (1 + az) and - z, where - 1 < a< 1 and α∈ R. We prove that such convolutions are locally univalent and convex in the horizontal direction under certain condition.

First Page

729

Last Page

736

DOI

10.1007/s00605-020-01442-3

Publication Date

12-1-2020

Recommended Citation

Ali, Md Firoz; Allu, Vasudevarao; and Ghosh, Nirupam, "A convolution property of univalent harmonic right half-plane mappings" (2020). Journal Articles. 51.
https://digitalcommons.isical.ac.in/journal-articles/51