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- Title
A Third-Order Differential Equation and Starlikeness of a Double Integral Operator.
- Authors
Ali, Rosihan M.; See Keong Lee; Subramanian, K. G.; Swaminathan, A.
- Abstract
Functions f(z) = z + ∑ Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. 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) = ∫Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.∫Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.G(ztµsv)t-µs-vds 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.
- Subjects
DIFFERENTIAL equations; INTEGRAL operators; UNIVALENT functions; CONVEX functions; IMAGE processing; MATHEMATICAL analysis
- Publication
Abstract & Applied Analysis, 2011, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2011/901235