A subclass of harmonic univalent functions with positive coefficients

  • K. K. Dixit
  • Saurabh Porwal

Abstract

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disc $U$ can be written in the form $f=h+\bar g$, where $h$ and $g$ are analytic in $U$. In this paper authors introduce the class, $R_H(\beta)$, $(1<\beta \le 2)$ consisting of harmonic univalent functions $f=h+\bar g$, where $h$ and $g$ are of the form $ h(z)=z+ \sum_{k=2}^\infty |a_k|z^k $ and $ g(z)= \sum_{k=1}^\infty |b_k| z^k $ for which $\Re\{h'(z)+g'(z)\}<\beta$. We obtain distortion bounds extreme points and radii of convexity for functions belonging to this class and discuss a class  preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combinations.

Author Biographies

K. K. Dixit
Department of Mathematics, Janta College, Bakewar, Etawah (U.P.) 206124, India.
Saurabh Porwal
Department of Mathematics, Janta College, Bakewar, Etawah (U.P.) 206124, India.
Published
2010-09-30
How to Cite
Dixit, K. K., & Porwal, S. (2010). A subclass of harmonic univalent functions with positive coefficients. Tamkang Journal of Mathematics, 41(3), 261-269. https://doi.org/10.5556/j.tkjm.41.2010.724
Section
Papers