Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra ( JLTA )2252-0201080320190801A new subclass of harmonic mappings with positive coefficients159165667307ENA. R.HaghighiDepartment of Mathematics, Technical and Vocational, University (TVU), Tehran, IranN.AsgharyDepartment of Mathematics, Islamic Azad University, Central Tehran Branch,
Tehran, IranA.SedghiDepartment of Mathematics, Islamic Azad University, Central Tehran Branch,
Tehran, IranJournal Article20181016Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk $U$ can be written as form $f =h+bar{g}$, where $h$ and $g$ are analytic in $U$. In this paper, we introduce the class $S_H^1(beta)$, where $1<betaleq 2$, and consisting of harmonic univalent function $f = h+bar{g}$, where $h$ and $g$ are in the form $h(z) = z+sumlimits_{n=2}^infty |a_n|z^n$ and $g(z) =sumlimits_{n=2}^infty |b_n|bar z^n$ for which $$mathrm{Re}left{z^2(h''(z)+g''(z)) +2z(h'(z)+g'(z))-(h(z)+g(z))-(z-1)right}<beta.$$ It is shown that the members of this class are convex and starlike. We obtain distortions bounds extreme point for functions belonging to this class, and we also show this class is closed under convolution and convex combinations.http://jlta.iauctb.ac.ir/article_667307_1d003b1f1b1aca872324712e9cdb6ded.pdf