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Radius Constants for Analytic Functions with Fixed Second Coefficient

Let f(z) = z + ∑(n=2) (∞) a (n) z (n) be analytic in the unit disk with the second coefficient a (2) satisfying |a (2) | = 2b, 0 ≤ b ≤ 1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies |a (n) | ≤ cn + d  (c, d ≥ 0) or |a (n) | ≤ c/n  (c > 0  and ...

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Detalles Bibliográficos
Autores principales: Nargesi, Mahnaz M., Ali, Rosihan M., Ravichandran, V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4102033/
https://www.ncbi.nlm.nih.gov/pubmed/25101327
http://dx.doi.org/10.1155/2014/898614
Descripción
Sumario:Let f(z) = z + ∑(n=2) (∞) a (n) z (n) be analytic in the unit disk with the second coefficient a (2) satisfying |a (2) | = 2b, 0 ≤ b ≤ 1. Sharp radius of Janowski starlikeness is obtained for functions f whose nth coefficient satisfies |a (n) | ≤ cn + d  (c, d ≥ 0) or |a (n) | ≤ c/n  (c > 0  and  n ≥ 3). Other radius constants are also obtained for these functions, and connections with earlier results are made.