On Harmonic Entire mappings

2021/04/01 by Deng, Hua, Qiao, Jinjing, Ponnusamy, Saminathan +1
#30D15 #30D20 #31A05 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 31A05 #Secondary: 30D10

paper · doi:10.48550/arxiv.2104.00414

Abstract

In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping f=h+g, respectively, and also consider the relationship between the order and the type of f, h, and g. Secondly, we investigate the harmonic mappings f=h+g such that f^(n_p)=h^(n_p)+g^(n_p) are univalent in the unit disk, where \n_p\_p=1^∞ be a strictly increasing sequence of nonnegative integers. In terms of the sequence \n_p\_p=1^∞, we derive several necessary conditions for these mappings to be entire and also establish an upper bound for the order of these mappings.

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