Properties of a class of \(p\)-harmonic functions. (English) Zbl 1470.30022

Summary: A \(p\) times continuously differentiable complex-valued function \(F = u + i v\) in a domain \(D \subseteq \mathbb{C}\) is \(p\)-harmonic if \(F\) satisfies the \(p\)-harmonic equation \(\Delta \cdots \Delta F = 0\), where \(p\) is a positive integer. By using the generalized Salagean differential operator, we introduce a class of \(p\)-harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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