On Lappan’s five-valued theorem for φ-normal functions in several variables - Datt, G. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.5 Let U^mC^m be а unit ball centered at the origin and let P^n be an n-dimensional complex projective space with the metric E_P^n. Also, let φ[0,1)→(0,∞) be a smoothly increasing function. A holomorphic mapping fU^m→ P^n is called φ-normal if (φ(\|z\|))^-1(E_P^n(f(z), df(z))(ξ)) is bounded above for zU^m and ξC^m such that \|ξ\|=1, where df(z) is the map from T_z(U^m) to T_f(z)(P^n) 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.