In this paper, we further investigate the class of functions ϕ * ( n, p, λ, α ) which are analytic in the open unit disk △ = { z : z 1}, 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 ϕ * ( n, p, λ, α ), 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 ϕ * ( n, p, λ, α ), we introduce the special class ϕc*(n,p,λ,α)$phi _c^* (n,p,lambda ,alpha )$ and discuss the extreme points.
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