The aim of this paper is to investigate some motivated geometrical aspects and properties of polyharmonic functions (PH) including starlikeness, convexity and univalence. A polyharmonicity preserving complex operator is also introduced. Further, a new subclass of polyharmonic functions (CPH) is defined and certain characteristics of elements of this subclass are examined and obtained. In particular, we extend Landau's theorem to functions in this subclass, and consider the Goodman–Saff conjecture and prove that the conjecture is true for mappings belonging to CPH.
Khuri, S. (2013). On the properties of a class of polyharmonic functions. Mathematical Modelling and Analysis, 18(2), 219-235. https://doi.org/10.3846/13926292.2013.781069
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.