Dirichlet problem, Univalency and Schwarz Lemma for Biharmonic Mappings
Zayid Abdulhadi, Yusuf Abu Muhanna, Saminathan Ponnusamy
TL;DR
This paper explores biharmonic mappings, establishing a Schwarz Lemma and conditions for univalency, thereby extending classical harmonic analysis results to biharmonic functions.
Contribution
It introduces a Schwarz Lemma for biharmonic mappings and investigates univalency within this class, providing new theoretical insights.
Findings
Schwarz Lemma holds for certain biharmonic mappings
Univalency conditions are identified for specific biharmonic classes
Maximum principle applies to the studied biharmonic family
Abstract
In this paper, we shall discuss the family of biharmonic mappings for which maximum principle holds. As a consequence of our study, we present Schwarz Lemma for the family of biharmonic mappings. Also we discuss the univalency of certain class of biharmonic mappings.
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