We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Geometric and Analytic Properties Associated With Extension Operators.
- Authors
Wang, Jianfei; Liu, Taishun; Zhang, Yanhui
- Abstract
The first aim is to prove that the Roper-Suffridge extension operator preserves ε -starlike property on general domains given by convex functions. The second is to construct the generalized Roper-Suffridge extension operator on Reinhard domains Ω p 1 , p 2 , ⋯ , p n = { (z 1 , ... , z n) ∈ C n : ∑ j = 1 n | z j | p j < 1 } , p 1 , ⋯ , p n ≥ 1. By using a refined Schwarz-Pick lemma, we prove that the operator preserves important properties, e.g., subordination property and spirallikeness. This solves a problem of Gong and Liu. Our result improves many known results from p 1 = 2 to 1 ≤ p 1 < ∞ . As applications, we obtain growth and covering results associated with the extension operator on p-unit ball. Finally, by obtaining geometric and analytic properties of bounded symmetric domains, we generalize the Pfaltzgraff-Suffridge extension operator over bounded symmetric domains and prove Loewner chains and starlikeness are also preserved with a new idea. Further, we propose two conjectures for convexity property.
- Subjects
SYMMETRIC domains; CONVEX functions; CONVEX domains; PROBLEM solving; STAR-like functions
- Publication
Journal of Geometric Analysis, 2024, Vol 34, Issue 6, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-024-01600-1