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Abstract and Applied Analysis
Volume 2013, Article ID 968627, 8 pages
Research Article

Properties of a Class of -Harmonic Functions

Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey

Received 21 January 2013; Accepted 21 May 2013

Academic Editor: Youyu Wang

Copyright © 2013 Elif Yaşar and Sibel Yalçın. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A times continuously differentiable complex-valued function in a domain is -harmonic if satisfies the -harmonic equation , where is a positive integer. By using the generalized Salagean differential operator, we introduce a class of -harmonic functions and investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points, and convex combination of the class.