Abstract and Applied Analysis

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

Rosihan M. Ali, See Keong Lee, K. G. Subramanian, and A. Swaminathan

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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 i t s t f ( z ) = 0 1 0 1 ? G ( z t μ s ν ) t - μ s - ν i t s 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 .

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 901235, 10 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171117

Digital Object Identifier
doi:10.1155/2011/901235

Mathematical Reviews number (MathSciNet)
MR2771238

Zentralblatt MATH identifier
1207.30012

Citation

Ali, Rosihan M.; Lee, See Keong; Subramanian, K. G.; Swaminathan, A. A Third-Order Differential Equation and Starlikeness of a Double Integral Operator. Abstr. Appl. Anal. 2011 (2011), Article ID 901235, 10 pages. doi:10.1155/2011/901235. https://projecteuclid.org/euclid.aaa/1313171117


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