## Abstract and Applied Analysis

### Properties of a Class of $p$-Harmonic Functions

#### Abstract

A $p$ times continuously differentiable complex-valued function $F=u+iv$ in a domain $D\subseteq ℂ$ is $p$-harmonic if $F$ satisfies the $p$-harmonic equation $\mathrm{\Delta }\cdots \mathrm{\Delta }F=0$, 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 968627, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511930

Digital Object Identifier
doi:10.1155/2013/968627

Mathematical Reviews number (MathSciNet)
MR3065769

Zentralblatt MATH identifier
07095544

#### Citation

Yaşar, Elif; Yalçın, Sibel. Properties of a Class of $p$ -Harmonic Functions. Abstr. Appl. Anal. 2013 (2013), Article ID 968627, 8 pages. doi:10.1155/2013/968627. https://projecteuclid.org/euclid.aaa/1393511930

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