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- W4385374210 abstract "In the present article, we discuss about the estimate of the pre-Schwarzian and Schwarzian norms for locally univalent harmonic functions $f=h+overline{g}$ in the unit disk $mathbb{D}:={zinmathbb{C}:, |z|<1}$. In this regard, we first rectify an earlier result of Kanas emph{et al.} [J. Math. Anal. Appl., {bf 474}(2) (2019), 931--943] and prove a general result for the pre-Schwarzian norm. We also consider a new class $mathcal{F}_0$ consisting of all harmonic functions $f=h+overline{g}$ in the unit disk $mathbb{D}$ such that ${rm Re,}left(1+zfrac{h''(z)}{h'(z)}right)>0$ for $zinmathbb{D}$ with dilatation $omega_f(z)in Aut(mathbb{D})$ and obtain best possible estimates of the pre-Schwarzian and Schwarzian norms for functions in the class $mathcal{F}_0$. Moreover, we obtain the distortion and coefficient estimates of the co-analytic function $g$ when $f=h+overline{g}inmathcal{F}_0$." @default.
- W4385374210 created "2023-07-29" @default.
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- W4385374210 date "2023-07-27" @default.
- W4385374210 modified "2023-10-16" @default.
- W4385374210 title "Pre-Schwarzian and Schwarzian norm estimates for harmonic functions with fixed analytic part" @default.
- W4385374210 doi "https://doi.org/10.48550/arxiv.2307.14793" @default.
- W4385374210 hasPublicationYear "2023" @default.
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