Convolutions of prestarlike functions

O. P. Ahuja and H. Silverman

International Journal of Mathematics and Mathematical Sciences, 1983, vol. 6, 1-10

Abstract:

The convolution of two functions f ( z ) = ∑ n = 0 ∞ a n z n and g ( z ) = ∑ n = 0 ∞ b n z n defined as ( f ∗ g ) ( z ) = ∑ n = 0 ∞ a n b n z n . For f ( z ) = z − ∑ n = 2 ∞ a n z n and g ( z ) = z / ( 1 − z ) 2 ( 1 − γ ) , the extremal function for the class of functions starlike of order γ , we investigate functions h , where h ( z ) = ( f ∗ g ) ( z ) , which satisfy the inequality | ( z h ′ / h ) − 1 | / | ( z h ′ / h ) + ( 1 - 2 α ) | < β , 0 ≤ α < 1 , 0 < β ≤ 1 for all z in the unit disk. Such functions f are said to be γ -prestarlike of order α and type β . We characterize this family in terms of its coefficients, and then determine extreme points, distortion theorems, and radii of univalence, starlikeness, and convexity. All results are sharp.

Date: 1983
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/6/987276.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/6/987276.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:987276

DOI: 10.1155/S0161171283000034

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 ().