Preprint
Sep 2026
On $\varphi$-Normality of Harmonic Mappings and Their Families
In this paper, we present Lappan's five-point type criteria for $\varphi$-normality of sense-preserving harmonic mappings and families of harmonic mappings in the unit disc $\mathbb{D}$. We establish a normality criterion involving the higher-order spherical derivative of order $k$, and $k+2$ distinct test values under...
Gopal Datt, Ritesh Pal
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