Absolutely convex, uniformly starlike and uniformly convex harmonic mappings

Authors

Saminathan Ponnusamy, Indian Statistical Institute Chennai
Anbareeswaran Sairam Kaliraj, Indian Statistical Institute Chennai
Victor V. Starkov, PetrSU

Article Type

Research Article

Publication Title

Complex Variables and Elliptic Equations

Abstract

In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disc. 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.

First Page

1418

Last Page

1433

DOI

10.1080/17476933.2016.1182518

Publication Date

10-2-2016

Recommended Citation

Ponnusamy, Saminathan; Sairam Kaliraj, Anbareeswaran; and Starkov, Victor V., "Absolutely convex, uniformly starlike and uniformly convex harmonic mappings" (2016). Journal Articles. 4084.
https://digitalcommons.isical.ac.in/journal-articles/4084