Absolutely Convex, Uniformly Starlike and Uniformly Convex Harmonic Mappings
Complex Variables
2016-05-10 v1
Abstract
In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disk. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hypergeometric and polylogarithm functions.
Keywords
Cite
@article{arxiv.1605.02171,
title = {Absolutely Convex, Uniformly Starlike and Uniformly Convex Harmonic Mappings},
author = {Saminathan Ponnusamy and Anbareeswaran Sairam Kaliraj and Victor V. Starkov},
journal= {arXiv preprint arXiv:1605.02171},
year = {2016}
}
Comments
16 pages; A version of it is appear in the journal: Complex Variables and Elliptic Equations