A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

A Third-Order Differential Equation and Starlikeness of a Double Integral Operator

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Functions f(z)=z+∑2∞‍anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(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 operat...

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Bibliographic Details
Main Authors: Rosihan M. Ali, See Keong Lee, K. G. Subramanian, A. Swaminathan
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/901235
Description
Summary:Functions f(z)=z+∑2∞‍anzn that are analytic in the unit disk and satisfy the differential equation f'(z)+αzf''(z)+γz2f'''(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)=∫01∫01‍G(ztμsν)t-μs-νds dt 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.
ISSN:1085-3375
1687-0409

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