ON REFINEMENT OF THE COEFFICIENT INEQUALITIES FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES

• 作者: Qinghua XU Yuanping LAI
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（6）
• 页码范围: 1653-1665
• 页数: 13页
• 语种: 英文

摘要

Let К be the familiar class of normalized convex functions in the unit disk. In [14], Keogh and Merkes proved that for a function f(z) = z + ∞∑k=2 akzk in the class К,|a3-λa22|≤ max{1/3.|λ-1|} , λ∈ C.The above estimate is sharp for each λ. In this article, we establish the corresponding inequality for a normalized convex function f on U such that z = 0 is a zero of order k+1 of f(z) - z, and then we extend this result to higher dimensions. These results generalize some known results.