TY - JOUR AU - Dixit, K. K. AU - Porwal, Saurabh PY - 2010/09/30 Y2 - 2024/03/28 TI - A subclass of harmonic univalent functions with positive coefficients JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 41 IS - 3 SE - Papers DO - 10.5556/j.tkjm.41.2010.724 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/724 SP - 261-269 AB - <p>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, $R_H(\beta)$, $(1&lt;\beta \le 2)$ 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 $\Re\{h'(z)+g'(z)\}&lt;\beta$. We obtain distortion bounds extreme points and radii of convexity for functions belonging to this class and discuss a class&nbsp; preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combinations.</p> ER -