期刊论文

Ponnusamy, Saminathan

英文

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

0362-546X

2015

123-124

178-190

10.1016/j.na.2014.06.005

The research and the visit of the first author to ISI Chennai Centre were supported by “Abel visiting Scholar Program” of Commission for Developing Countries (IMU). The research was also supported by NSF of China (No. 11201130 ), Hunan Provincial Natural Science Foundation of China (No. 14JJ1012 ) and construct program of the key discipline in Hunan province. The second author is currently on leave from the Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India.

本校为第一机构

In this article, we consider the class SHC of normalized stable harmonic convex mappings f=h+g¯ in the unit disk and determine r such that every section of f is close-to-convex or convex in the disk ∣z∣<r. Also, we show that the convolution f∗f∈SHC whenever f∈SHC. In addition, we prove that the harmonic convolution f1∗f2 is stable harmonic close-to-convex whenever f1∈SHC and f2 is either a slanted half-plane mapping or an asymmetric vertical strip mapping or a mapping in the family PH 0(α) which is contained in the family of harmonic ...