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a new subclass of harmonic mappings with positive coefficients
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نویسنده
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haghighi a. r. ,asghary n. ,sedghi a.
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منبع
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journal of linear and topological algebra - 2019 - دوره : 8 - شماره : 3 - صفحه:159 -165
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چکیده
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complexvalued harmonic functions that are univalent and sensepreserving 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 $$mathrm{re}left{z^2(h’’(z)+g’’(z)) +2z(h’(z)+g’(z))(h(z)+g(z))(z1)right}<beta.$$ 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.
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کلیدواژه
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convex combinations ,extreme points ,harmonic starlike functions ,harmonic univalent functions
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آدرس
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technical and vocational university (tvu), department of mathematics, iran, islamic azad university, central tehran branch, department of mathematics, iran, islamic azad university, central tehran branch, department of mathematics, iran
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پست الکترونیکی
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ali_sedghi1389@yahoo.com
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Authors
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