Subordination criteria for starlikeness and convexity

Rasoul Aghalary and Jay M. Jahangiri

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-7

Abstract:

For functions p analytic in the open unit disc U = { z : | z | < 1 } with the normalization p ( 0 ) = 1 , we consider the families 𝒫 [ A , − 1 ] , − 1 < A ≤ 1 , consisting of p such that p ( z ) is subordinate to ( 1 + A z ) / ( 1 − z ) in U and 𝒫 ( 1 , b ) , b > 0 , consisting of p , which have the disc formulation | p − 1 | < b in U . We then introduce subordination criteria for the choice of p ( z ) = z f ′ ( z ) / f ( z ) , where f is analytic in U and normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 . We also obtain starlikeness and convexity conditions for such functions f and consequently extend and, in some cases, improve the corresponding previously known results.

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/486901.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/486901.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:486901

DOI: 10.1155/S0161171203207146

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 ().