A subclass of harmonic univalent functions with negative coefficients

Karpuzogullari S., Ozturk M., Yamankaradeniz M.

APPLIED MATHEMATICS AND COMPUTATION, vol.142, pp.469-476, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 142
  • Publication Date: 2003
  • Doi Number: 10.1016/s0096-3003(02)00314-4
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.469-476
  • Keywords: harmonic functions, extreme points, distortion bounds
  • Bursa Uludag University Affiliated: Yes

Abstract

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, consider the class HP(beta), (0 less than or equal to beta < 1) consisting of harmonic and univalent functions f = h + (g) over bar for which Re{ h'(z) + g'(z)} > beta. We give sufficient coefficient conditions for normalized harmonic functions in the class HP(beta). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points. (C) 2002 Elsevier Science Inc. All rights reserved.