Convolutions of harmonic half-plane mappings with harmonic vertical strip mappings
نویسندگان
چکیده
منابع مشابه
On the Linear Combinations of Slanted Half-Plane Harmonic Mappings
In this paper, the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.
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Let fβ = hβ + gβ and Fa = Ha +Ga be harmonic mappings obtained by shearing of analytic mappings hβ + gβ = 1/(2isinβ) log ( (1 + ze)/(1 + ze) ) , 0 < β < π and Ha+Ga = z/(1 − z), respectively. Kumar et al. [7] conjectured that if ω(z) = ez(θ ∈ R, n ∈ N) and ωa(z) = (a − z)/(1 − az), a ∈ (−1, 1) are dilatations of fβ and Fa, respectively, then Fa∗̃fβ ∈ S 0 H and is convex in the direction of the r...
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ژورنال
عنوان ژورنال: Filomat
سال: 2017
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1707843l