Abstract
In this paper, we introduce and study a subclass of harmonic univalent functions defined by a differential operator in the unit disk U = {z ∈ C: |z| = 1}. Also we obtain the coefficient bounds, extreme points, convex combination and convolution conditions.
Highlights
In this paper we find that many results of Özturk and Yalcin [5] are incorrect
Results concerning the convolutions of functions satisfying the above inequalities with univalent, harmonic and convex functions in the unit disc and harmonic functions having positive real part are obtained
Let U denote the open unit disc and SH denote the class of all complex valued, harmonic, orientation-preserving, univalent functions f in U normalized by f (0) = fz(0) − 1 = 0
Summary
Received: Accepted: Communicated by: 2000 AMS Sub. Class.: Key words: Abstract: 04 June, 2008 27 September, 2008 H.M. Srivastava 30C45, 31A05. The class of univalent harmonic functions on the unit disc satisfying the condition. Sharp coefficient relations and distortion theorems are given for these functions. In this paper we find that many results of Özturk and Yalcin [5] are incorrect. Some of the results of this paper correct the theorems and examples of [5]. Sharp coefficient relations and distortion theorems are given. Results concerning the convolutions of functions satisfying the above inequalities with univalent, harmonic and convex functions in the unit disc and harmonic functions having positive real part are obtained. Harmonic Univalent Functions K.K. Dixit and Saurabh Porwal vol 10, iss.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
