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.
