ON SCHWARZ-PICK TYPE INEQUALITY FOR MAPPINGS SATISFYING POISSON DIFFERENTIAL INEQUALITY

• 作者: Deguang ZHONG Fanning MENG Wenjun YUAN
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（3）
• 页码范围: 959-967
• 页数: 9页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.03.020

摘要

Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)|≤B·|Df(z)|2 for some B＞0 and f(0)= 0.In this note,we show that f does not always satisfy the Schwarz-Pick type inequality 1-|z|2/1-|f(z)|2≤C{B),where C(B)is a constant depending only on B.Moreover,a more general Schwarz-Pick type inequality for mapping that satisfies general Poisson differential inequality is established under certain conditions.