On Multivalent Harmonic Functions with Positive Ositive Real Part
Sibel Yalin and Metin ztürk* Author for corresponding; e-mail address: skarpuz@uludag.edu.tr
Volume: Vol.34 No.3 (SEPTEMBER 2007)
Research Article
DOI:
Received: 20 May 2007, Revised: -, Accepted: 30 September 2007, Published: -
Citation: Yalin S. and Ztürk M., On Multivalent Harmonic Functions with Positive Ositive Real Part, Chiang Mai Journal of Science, 2007; 34(3): 273-279.
Abstract
New classes of complex-valued, multivalent harmonic functions of the form f = h + g , where h and g are multivalent analytic in the unit disk are introduced. We give sufficient conditions for these classes. These coefficient conditions are shown to be also necessary if the coefficients of h and g of the harmonic functions f = h + g are negative. Furthermore, we determine a representation theorem, extreme points, distortion and covering theorems, convolution conditions and convex combinations for these functions.