Approximation properties of univalent mappings on the unit ball in C-n

作者：Hamada H^*; Iancu M; Kohr G; Schleissinger S

来源：Journal of Approximation Theory, 2018, 226: 14-33.

DOI：10.1016/j.jat.2017.11.005

• Automorphism
• Convex mapping
• Loewner differential equation
• Parametric representation
• Spirallike mapping
• Starlike mapping

Let n >= 2. In this paper, we obtain approximation properties of various families of normalized univalent mappings f on the Euclidean unit ball B-n in C-n by automorphisms of C-n whose restrictions to B-n have the same geometric property of f. First, we obtain approximation properties of spirallike, convex and g-starlike mappings f on B-n by automorphisms of C-n whose restrictions to 3 n have the same geometric property of f, respectively. Next, for a nonresonant operator A with m(A) > 0, we obtain an approximation property of mappings which have A-parametric representation by automorphisms of C-n whose restrictions to 10 have A-parametric representation. Certain questions will be also mentioned. Finally, we obtain an approximation property by automorphisms of C-n for a subset of S-In(0) (B-n) consisting of mappings f which satisfy the condition parallel to Df(z) - I-n parallel to < 1, z is an element of B-n. Related results will be also obtained.

• 出版日期2018-2