Directional Convexity of Convolutions of Harmonic Functions. (1st April 2019)

• Record Type: Journal Article
• Authors: Jahangiri, Jay M.; Garg, Raj Kumar
• Other Names: Bulboaca Teodor Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2019(2019)
• Publication Date: 2019-04-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2019/5731830
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Harmonic functions can be constructed using two analytic functions acting as their analytic and coanalytic parts but the prediction of the behavior of convolution of harmonic functions, unlike the convolution of analytic functions, proved to be challenging. In this paper we use the shear construction of harmonic mappings and introduce dilatation conditions that guarantee the convolution of two harmonic functions to be harmonic and convex in the direction of imaginary axis.