On harmonic bloch and normal functions

Ozturk M., Yalcin S.

Indian Journal of Pure and Applied Mathematics, cilt.36, sa.8, ss.407-416, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 8
  • Basım Tarihi: 2005
  • Dergi Adı: Indian Journal of Pure and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.407-416
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

Let f = h + ḡ be a harmonic univalent and sense preserving function on the unit disk, where h and g are analytic. We give the definition of a normal harmonic function. The necessary and sufficient conditions for f = h + ḡ to be Bloch or normal are determined. The sharp upper bound for | f (z) | is obtained whenever f = h + ḡ is a Bloch function. We obtain sharp estimates for the normality order of f when f maps the unit disk onto the unit disk.