Making use of a linear operator Iλp(a,c), which is defined here by means of the Hadamard product (or convolution), we introduce some new subclasses of multivalent functions and investigate various inclusion properties of these subclasses. Some radius problems are also discussed.
S. D. Bernardi, “Convex and Starlike Univalent Functions,” Transactions of the American Mathematical Society, Vol. 135, 1969, pp. 429-446.
doi:10.1090/S0002-9947-1969-0232920-2
B. C. Carlson and D. B. Shaffer, “Starlike and Prestarlike Hypergeometric Functions,” SIAM Journal on Mathematical Analysis, Vol. 15, No. 4, 1984, pp. 737-745.
doi:10.1137/0515057
N. K. Cho, O. S. Kwon and H. M. Srivastava, “Inclusion Relationships and Argument Properties for Certain Subclasses of Multivalent Functions Associated with a Family of Linear Operator,” Journal of Mathematical Analysis and Applications, Vol. 292, No. 2, 2004, pp. 470-483.
doi:10.1016/j.jmaa.2003.12.026
S. S. Miller, “Differen-tial Inequalities and Caratheodory Functions,” Bulletin of the American Mathematical Society, Vol. 81, 1975, pp. 78-81.
doi:10.1090/S0002-9904-1975-13643-3
K. I. Noor, “On Subclasses of Close-to-Convex Functions of Higher Order,” International Journal of Mathematics and Mathematical Sci-ences, Vol. 15, No. 2, 1992, pp. 279-289. doi:10.1155/S016117129200036X
K. I. Noor and M. Arif, “Gen-eralized Integral Operators Related with p-Valent Analytic Functions,” Mathematical Inequalities Applications, Vol. 12, No. 1, 2009, pp. 91-98.
J. Patal and N. E. Cho, “Some Classes of Analytic Functions Involving Noor Integral Opera-tor,” Journal of Mathematical Analysis and Applications, Vol. 312, No. 2, 2005, pp. 564-575. doi:10.1016/j.jmaa.2005.03.047
J. Sokó? and L. Trojnar-Spelina, “Convolution Properties for Certain Classes of Multivalent Functions,” Journal of Mathematical Analysis and Applications, Vol. 337, No. 2, 2008, pp. 1190-1197. doi:10.1016/j.jmaa.2007.04.055
