A class of univalent functions with varying arguments

K. S. Padmanabhan and M. Jayamala

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-6

Abstract:

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.

Date: 1992
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/15/453427.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/15/453427.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:453427

DOI: 10.1155/S016117129200067X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().