In:
International Journal of Mathematics and Mathematical Sciences, Hindawi Limited, Vol. 32, No. 5 ( 2002), p. 319-324
Abstract:
An analytic function f ( z ) = z + a n + 1 z n + 1 + ⋯ , defined on the unit disk △ = { z : | z | 〈 1 } , is in the class S p if z f ′ ( z ) / f ( z ) is in the parabolic region Re w 〉 | w − 1 | . This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in S p are obtained. In particular, we find condition on λ such that the function f ( z ) , satisfying ( 1 − α ) ( f ( z ) / z ) μ + α f ′ ( z ) ( f ( z ) / z ) μ − 1 ≺ 1 + λ z , is in S p .
Type of Medium:
Online Resource
ISSN:
0161-1712
,
1687-0425
DOI:
10.1155/S0161171202007895
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2002
detail.hit.zdb_id:
1492203-4
SSG:
17,1
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