Abstract. In the present paper, using Jack0
lemma, the authors investigate the differential inequality
|(1 − α)
L
λ+1
a
f(z)
z
+ α
L
λ
a
f(z)
L
λ+1
a f(z)
− 1| < µ, z ∈ U,
regarding univalent functions defined by integral operator in the open unit
disk U = {z : |z| < 1}. As consequences, sufficient conditions for univalence, starlikeness and strongly starlikeness of certain analytic functions are
obtained.