Let 𝕌m ⊂ ℂm be a unit ball centered at the origin and let ℙn be an n-dimensional complex projective space with the metric Eℙn. Moreover, let φ: [0, 1) → (0,∞) be a smoothly increasing function. A holomorphic mapping f : 𝕌m → ℙn is called φ-normal if (φ||z||))−1(Eℙn(f(z), df (z))(ξ)) is bounded above for z ∈ 𝕌m and ξ ∈ ℂm such that ||ξ|| = 1, where df (z) is a map from Tz(𝕌m) into Tf(z) (ℙn) induced by f. For n = 1, f is called a φ-normal function. We present an extension of Lappan’s five-valued theorem to the class of φ-normal functions.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 9, pp. 1284–1290, September, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i9.6237.
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Datt, G. On Lappan’s Five-Valued Theorem for φ-Normal Functions of Several Variables. Ukr Math J 74, 1463–1470 (2023). https://doi.org/10.1007/s11253-023-02147-0
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DOI: https://doi.org/10.1007/s11253-023-02147-0