Criteria of univalence and fully –accessibility for p–harmonic and p–analytic functions

Abstract

In this article, we present univalence criteria for polyharmonic and polyanalytic functions. Our approach yields a new criterion for a polyharmonic functions to be fully -accessible. Several examples are presented to illustrate the use of these criteria.

Keywords:

• Univalence
• p-harmonic
• p-analytic function
• fully -accessible function
• -accessible domain
• starlike domain and Elliptic PDE

AMS Subject Classifications:

• Primary: 31A05
• 31A30
• 31C05
• 30C45
• 52A30
• Secondary: 30C20

Acknowledgements

The authors thank Sh. Chen, S. Yu. Graf, Sairam Kaliraj, and V. V. Starkov for fruitful discussion and comments on this manuscript.

Notes

The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

Funding

The research was supported by the project RUS/RFBR/P-163 under Department of Science and Technology. The first and the second authors were supported by Strategic Development Program of Petrozavodsk State University. The second author was supported by a grant from the Simons Foundation and RFBR [project N 14-01-00510a]. The third author is currently on leave from Indian Institute of Technology Madras.