A new subclass of complex harmonic functions

Yalcin S., Ozturk M.

MATHEMATICAL INEQUALITIES & APPLICATIONS, vol.7, no.1, pp.55-61, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 1
  • Publication Date: 2004
  • Doi Number: 10.7153/mia-07-07
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.55-61
  • Keywords: harmonic functions, univalent functions, extreme points, distortion bounds, UNIVALENT-FUNCTIONS
  • Bursa Uludag University Affiliated: Yes


Complex valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h + (g) over bar, where h and g are analytic in U. In this paper, we introduce a class HP(alpha), (alpha greater than or equal to 0) of functions which are harmonic in U. We give sufficient coefficient conditions for normalized harmonic functions in HP(alpha). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.