Opuscula Mathematica
Opuscula Math. 33, no. 2 (2013), 273-281

A unified representation of some starlike and convex harmonic functions with negative coefficients

R. M. El-Ashwah
M. K. Aouf
A. A. M. Hassan
A. H. Hassan
Abstract. In this paper we introduce a unified representation of starlike and convex harmonic functions with negative coefficients, related to uniformly starlike and uniformly convex analytic functions. We obtain extreme points, distortion bounds, convolution conditions and convex combinations for this family.
Keywords: harmonic, analytic, univalent, sense-preserving, extreme points.
Mathematics Subject Classification: 30C45.
Full text (pdf)
About the authors ▼
R. M. El-Ashwah
Damietta University, Faculty of Science, Department of Mathematics, New Damietta 34517, Egypt
M. K. Aouf
Mansoura University, Faculty of Science, Department of Mathematics, Mansoura 33516, Egypt
A. A. M. Hassan
Zagazig University, Faculty of Science, Department of Mathematics, Zagazig 44519, Egypt
A. H. Hassan
Zagazig University, Faculty of Science, Department of Mathematics, Zagazig 44519, Egypt
About the article ▼
Received: 2012-06-23.
Revised: 2012-10-29.
Accepted: 2012-10-29.
Cite this article as ▼
R. M. El-Ashwah, M. K. Aouf, A. A. M. Hassan, A. H. Hassan, A unified representation of some starlike and convex harmonic functions with negative coefficients, Opuscula Math. 33, no. 2 (2013), 273-281, http://dx.doi.org/10.7494/OpMath.2013.33.2.273.
Download this article's citation as: