Region of variability of univalent functions f(z) for which zf '(z) is spirallike

• Autores: Saminathan Ponnusamy, A. Vasudevarao, Hiroshi Yanagihara
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 4, 2008, págs. 1037-1048
• Idioma: inglés
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• Resumen

  • For a complex number a with Re(a) >0 let Sa(?) be the class of analytic functions f in the unit dist D with f(0)=0=f'(0)-1, f''(0)=2?e-iacos(a) satisfying Re eia(1+zf''(z)/f'(z))>0 for z in D. For a in D fixed, we determine the region of variability for log(f'(a)) when f ranges over the class Sa(?). As a consequence, we obtain an estimate for a pre-Schwarzian norm for Sa(0).