A subclass of harmonic univalent functions with negative coefficients

Karpuzogullari S., Ozturk M., Yamankaradeniz M.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 142
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1016/s0096-3003(02)00314-4
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.469-476
  • Anahtar Kelimeler: harmonic functions, extreme points, distortion bounds
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.