In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2011 ( 2011), p. 1-10
Abstract:
Functions f ( z ) = z + ∑ 2 ∞ a n z n that are analytic in the unit disk and satisfy the differential equation f ' ( z ) + α zf '' ( z ) + γ z 2 f ' '' ( z ) = g ( z ) are considered, where g is subordinated to a normalized convex univalent function h . These functions f are given by a double integral operator of the form f ( z ) = ∫ 0 1 ∫ 0 1 G ( z t μ s ν ) t - μ s - ν ds d t with G ' subordinated to h . The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function h .
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2011
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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