期刊论文

Li, Liulan

英文

Czechoslovak Mathematical Journal

0011-4642

2016

66

2

331-350

10.1007/s10587-016-0259-9

The visit and research of the first author was supported by “Abel visiting Scholar Program” of Commission for Developing Countries (IMU). The research was also supported by NSF of China (Nos. 11201130 and 11571216), Hunan Provincial Natural Science Foundation of China (No. 14JJ1012), and the construct program of the key discipline in Hunan province. The second author is currently on leave from the Indian Institute of Technology Madras.

本校为第一且通讯机构

We consider the class H 0 of sense-preserving harmonic functions $$f = h + \bar g$$ defined in the unit disk |z| < 1 and normalized so that h(0) = 0 = h′(0) − 1 and g(0) = 0 = g′(0), where h and g are analytic in the unit disk. In the first part of the article we present two classes P H 0(α) and G H 0(β) of functions from H 0 and show that if f ∈ P H 0(α) and F ∈ G H 0(β), then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions fo...