Abstract: Bernardi has proved that if f(z) is starlike univalent in the unit disk △, then so is the function g(z) given by
g(z)=(c+1)z^-1∫0^zt^c-1f(t)dt,c=1,2….In this paper, we extend Bernardi's theorem to certain class Φ_p^*(α,β,γ,ε,η;A) of p-valent starlike functions for operators. We prove that if f(A)∈Φ_p^*(α,β,γ,ε,η;A), then g(A), defined by
g(_A)=(p+c)∫₀¹t^c-1f(tA)dt,c=1,2,… also belongs to Φ_p^*(α,β,γ,ε,η;A) and give a sufficient and necessary vondition with reference to f(A) ∈Φ_p^*(α,β,γ,ε,η;A).