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  • 标题:A class of univalent functions with varying arguments
  • 本地全文:下载
  • 作者:K. S. Padmanabhan ; M. Jayamala
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:1992
  • 卷号:15
  • 期号:3
  • 页码:517-522
  • DOI:10.1155/S016117129200067X
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    f ( z ) = z + ∑ m = 2 ∞ a m z m is said to be in V ( θ n ) if the analytic and univalent function f in the unit disc E is nozmalised by f ( 0 ) = 0 , f ′ ( 0 ) = 1 and arg a n = θ n for all n . If further there exists a real number β such that θ n + ( n − 1 ) β ≡ π ( mod 2 π ) then f is said to be in V ( θ n , β ) . The union of V ( θ n , β ) taken over all possible sequence { θ n } and all possible real number β is denoted by V . V n ( A , B ) consists of functions f ∈ V such that D n + 1 f ( z ) D n f ( z ) = 1 + A w ( z ) 1 + B w ( z ) , − 1 ≤ A < B ≤ 1 , where n ∈ N U { 0 } and w ( z ) is analytic, w ( 0 ) = 0 and | w ( z ) | < 1 , z ∈ E . In this paper we find the coefficient inequalities, and prove distortion theorems.

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