In this paper, we further investigate the class of functions (…) which are analytic in the open unit disk (…),and involve the combinations of the representations of p-valently starlike and convex functions. We obtain several generalized results on the modified-Hadamard product of the class (…) which extend the corresponding results obtained by Altintas et al. [Computers Math. Applic. 30(2), 9-16, (1995)]; Darwish, Aouf [Mathematical and Computer Modelling (2007), doi:10.1016/j.mcm.2007.08.016 ]. Futher, by fixing the second coefficient of functions in (…) we introduce the special class (…) and discuss the extreme points.
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In this paper, we investigate the various important prop-erties and characteristics of the subclasses Sn (p, q, α, β) and Cn (p, q, α, β) of multivalent functions with negative coefficients defined by using a differential operator. We also derive many results for the modified Hadamard products of functions belongingto the classes Sn(p, q, α, β) and Cn(p, q, α, β). Finally several applications involving an integral operator and certain fractional calculus operators are also considered.
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