Partial sums of starlike harmonic univalent functions. (English) Zbl 1206.30030

Porwal, Saurabh; Dixit, Kaushal Kishore

Kyungpook Math. J. 50, No. 3, 433-445 (2010).

Summary: Although interesting properties of the partial sums of analytic univalent functions have been investigated extensively by several researchers, analogous results for the partial sums of harmonic univalent functions are not yet established so far. The main purpose of the present paper is to establish some new and interesting results on the ratio of a starlike harmonic univalent function to its sequence of partial sums.

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

harmonic function; univalent function; starlike function; partial sums